From a43bdb46c776cf183181c9a50f3702e1aa15da52 Mon Sep 17 00:00:00 2001
From: Philip Wadler <wadler@inf.ed.ac.uk>
Date: Fri, 14 Jul 2017 10:56:59 +0100
Subject: [PATCH] fixed backticks in code spans
---
out/Stlc.md | 3586 +++++++++++++-------------
out/StlcProp.md | 6108 ++++++++++++++++++++++----------------------
src/Stlc.lagda | 4 +-
src/StlcProp.lagda | 4 +-
4 files changed, 4851 insertions(+), 4851 deletions(-)
diff --git a/out/Stlc.md b/out/Stlc.md
index 5d615dea..97120503 100644
--- a/out/Stlc.md
+++ b/out/Stlc.md
@@ -366,7 +366,7 @@ And here it is formalised in Agda.
</pre>
Terms have six constructs. Three are for the core lambda calculus:
- * Variables, `\` x`
+ * Variables, `` ` x ``
* Abstractions, `λ[ x ∶ A ] N`
* Applications, `L · M`
and three are for the base type, booleans:
@@ -390,213 +390,213 @@ Here is the syntax of terms in BNF.
<pre class="Agda">
-<a name="3420" class="Keyword"
+<a name="3423" class="Keyword"
>infixl</a
- ><a name="3426"
- > </a
- ><a name="3427" class="Number"
- >20</a
><a name="3429"
> </a
- ><a name="3430" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="3430" class="Number"
+ >20</a
+ ><a name="3432"
+ > </a
+ ><a name="3433" href="Stlc.html#3556" class="InductiveConstructor Operator"
>_·_</a
- ><a name="3433"
+ ><a name="3436"
>
</a
- ><a name="3434" class="Keyword"
+ ><a name="3437" class="Keyword"
>infix</a
- ><a name="3439"
+ ><a name="3442"
> </a
- ><a name="3441" class="Number"
+ ><a name="3444" class="Number"
>15</a
- ><a name="3443"
+ ><a name="3446"
> </a
- ><a name="3444" href="Stlc.html#3517" class="InductiveConstructor Operator"
+ ><a name="3447" href="Stlc.html#3520" class="InductiveConstructor Operator"
>λ[_∶_]_</a
- ><a name="3451"
+ ><a name="3454"
>
</a
- ><a name="3452" class="Keyword"
+ ><a name="3455" class="Keyword"
>infix</a
- ><a name="3457"
+ ><a name="3460"
> </a
- ><a name="3459" class="Number"
+ ><a name="3462" class="Number"
>15</a
- ><a name="3461"
+ ><a name="3464"
> </a
- ><a name="3462" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="3465" href="Stlc.html#3612" class="InductiveConstructor Operator"
>if_then_else_</a
- ><a name="3475"
+ ><a name="3478"
>
</a
- ><a name="3477" class="Keyword"
+ ><a name="3480" class="Keyword"
>data</a
- ><a name="3481"
+ ><a name="3484"
> </a
- ><a name="3482" href="Stlc.html#3482" class="Datatype"
+ ><a name="3485" href="Stlc.html#3485" class="Datatype"
>Term</a
- ><a name="3486"
+ ><a name="3489"
> </a
- ><a name="3487" class="Symbol"
+ ><a name="3490" class="Symbol"
>:</a
- ><a name="3488"
+ ><a name="3491"
> </a
- ><a name="3489" class="PrimitiveType"
+ ><a name="3492" class="PrimitiveType"
>Set</a
- ><a name="3492"
+ ><a name="3495"
> </a
- ><a name="3493" class="Keyword"
+ ><a name="3496" class="Keyword"
>where</a
- ><a name="3498"
+ ><a name="3501"
>
</a
- ><a name="3501" href="Stlc.html#3501" class="InductiveConstructor"
+ ><a name="3504" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
- ><a name="3502"
+ ><a name="3505"
> </a
- ><a name="3503" class="Symbol"
+ ><a name="3506" class="Symbol"
>:</a
- ><a name="3504"
- > </a
- ><a name="3505" href="Maps.html#2171" class="Datatype"
- >Id</a
><a name="3507"
> </a
- ><a name="3508" class="Symbol"
- >→</a
- ><a name="3509"
+ ><a name="3508" href="Maps.html#2171" class="Datatype"
+ >Id</a
+ ><a name="3510"
> </a
- ><a name="3510" href="Stlc.html#3482" class="Datatype"
+ ><a name="3511" class="Symbol"
+ >→</a
+ ><a name="3512"
+ > </a
+ ><a name="3513" href="Stlc.html#3485" class="Datatype"
>Term</a
- ><a name="3514"
+ ><a name="3517"
>
</a
- ><a name="3517" href="Stlc.html#3517" class="InductiveConstructor Operator"
+ ><a name="3520" href="Stlc.html#3520" class="InductiveConstructor Operator"
>λ[_∶_]_</a
- ><a name="3524"
+ ><a name="3527"
> </a
- ><a name="3525" class="Symbol"
+ ><a name="3528" class="Symbol"
>:</a
- ><a name="3526"
- > </a
- ><a name="3527" href="Maps.html#2171" class="Datatype"
- >Id</a
><a name="3529"
> </a
- ><a name="3530" class="Symbol"
- >→</a
- ><a name="3531"
+ ><a name="3530" href="Maps.html#2171" class="Datatype"
+ >Id</a
+ ><a name="3532"
> </a
- ><a name="3532" href="Stlc.html#2531" class="Datatype"
+ ><a name="3533" class="Symbol"
+ >→</a
+ ><a name="3534"
+ > </a
+ ><a name="3535" href="Stlc.html#2531" class="Datatype"
>Type</a
- ><a name="3536"
+ ><a name="3539"
> </a
- ><a name="3537" class="Symbol"
+ ><a name="3540" class="Symbol"
>→</a
- ><a name="3538"
+ ><a name="3541"
> </a
- ><a name="3539" href="Stlc.html#3482" class="Datatype"
+ ><a name="3542" href="Stlc.html#3485" class="Datatype"
>Term</a
- ><a name="3543"
+ ><a name="3546"
> </a
- ><a name="3544" class="Symbol"
+ ><a name="3547" class="Symbol"
>→</a
- ><a name="3545"
+ ><a name="3548"
> </a
- ><a name="3546" href="Stlc.html#3482" class="Datatype"
+ ><a name="3549" href="Stlc.html#3485" class="Datatype"
>Term</a
- ><a name="3550"
+ ><a name="3553"
>
</a
- ><a name="3553" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="3556" href="Stlc.html#3556" class="InductiveConstructor Operator"
>_·_</a
- ><a name="3556"
+ ><a name="3559"
> </a
- ><a name="3557" class="Symbol"
+ ><a name="3560" class="Symbol"
>:</a
- ><a name="3558"
+ ><a name="3561"
> </a
- ><a name="3559" href="Stlc.html#3482" class="Datatype"
+ ><a name="3562" href="Stlc.html#3485" class="Datatype"
>Term</a
- ><a name="3563"
+ ><a name="3566"
> </a
- ><a name="3564" class="Symbol"
+ ><a name="3567" class="Symbol"
>→</a
- ><a name="3565"
+ ><a name="3568"
> </a
- ><a name="3566" href="Stlc.html#3482" class="Datatype"
+ ><a name="3569" href="Stlc.html#3485" class="Datatype"
>Term</a
- ><a name="3570"
+ ><a name="3573"
> </a
- ><a name="3571" class="Symbol"
+ ><a name="3574" class="Symbol"
>→</a
- ><a name="3572"
+ ><a name="3575"
> </a
- ><a name="3573" href="Stlc.html#3482" class="Datatype"
+ ><a name="3576" href="Stlc.html#3485" class="Datatype"
>Term</a
- ><a name="3577"
+ ><a name="3580"
>
</a
- ><a name="3580" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="3583" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="3584"
+ ><a name="3587"
> </a
- ><a name="3585" class="Symbol"
+ ><a name="3588" class="Symbol"
>:</a
- ><a name="3586"
+ ><a name="3589"
> </a
- ><a name="3587" href="Stlc.html#3482" class="Datatype"
+ ><a name="3590" href="Stlc.html#3485" class="Datatype"
>Term</a
- ><a name="3591"
+ ><a name="3594"
>
</a
- ><a name="3594" href="Stlc.html#3594" class="InductiveConstructor"
+ ><a name="3597" href="Stlc.html#3597" class="InductiveConstructor"
>false</a
- ><a name="3599"
+ ><a name="3602"
> </a
- ><a name="3600" class="Symbol"
+ ><a name="3603" class="Symbol"
>:</a
- ><a name="3601"
+ ><a name="3604"
> </a
- ><a name="3602" href="Stlc.html#3482" class="Datatype"
+ ><a name="3605" href="Stlc.html#3485" class="Datatype"
>Term</a
- ><a name="3606"
+ ><a name="3609"
>
</a
- ><a name="3609" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="3612" href="Stlc.html#3612" class="InductiveConstructor Operator"
>if_then_else_</a
- ><a name="3622"
+ ><a name="3625"
> </a
- ><a name="3623" class="Symbol"
+ ><a name="3626" class="Symbol"
>:</a
- ><a name="3624"
+ ><a name="3627"
> </a
- ><a name="3625" href="Stlc.html#3482" class="Datatype"
+ ><a name="3628" href="Stlc.html#3485" class="Datatype"
>Term</a
- ><a name="3629"
+ ><a name="3632"
> </a
- ><a name="3630" class="Symbol"
+ ><a name="3633" class="Symbol"
>→</a
- ><a name="3631"
+ ><a name="3634"
> </a
- ><a name="3632" href="Stlc.html#3482" class="Datatype"
+ ><a name="3635" href="Stlc.html#3485" class="Datatype"
>Term</a
- ><a name="3636"
+ ><a name="3639"
> </a
- ><a name="3637" class="Symbol"
+ ><a name="3640" class="Symbol"
>→</a
- ><a name="3638"
+ ><a name="3641"
> </a
- ><a name="3639" href="Stlc.html#3482" class="Datatype"
+ ><a name="3642" href="Stlc.html#3485" class="Datatype"
>Term</a
- ><a name="3643"
+ ><a name="3646"
> </a
- ><a name="3644" class="Symbol"
+ ><a name="3647" class="Symbol"
>→</a
- ><a name="3645"
+ ><a name="3648"
> </a
- ><a name="3646" href="Stlc.html#3482" class="Datatype"
+ ><a name="3649" href="Stlc.html#3485" class="Datatype"
>Term</a
>
@@ -613,225 +613,225 @@ CONTINUE FROM HERE
Example terms.
<pre class="Agda">
-<a name="3872" href="Stlc.html#3872" class="Function"
+<a name="3875" href="Stlc.html#3875" class="Function"
>f</a
- ><a name="3873"
+ ><a name="3876"
> </a
- ><a name="3874" href="Stlc.html#3874" class="Function"
+ ><a name="3877" href="Stlc.html#3877" class="Function"
>x</a
- ><a name="3875"
+ ><a name="3878"
> </a
- ><a name="3876" class="Symbol"
+ ><a name="3879" class="Symbol"
>:</a
- ><a name="3877"
- > </a
- ><a name="3878" href="Maps.html#2171" class="Datatype"
- >Id</a
><a name="3880"
+ > </a
+ ><a name="3881" href="Maps.html#2171" class="Datatype"
+ >Id</a
+ ><a name="3883"
>
</a
- ><a name="3881" href="Stlc.html#3872" class="Function"
+ ><a name="3884" href="Stlc.html#3875" class="Function"
>f</a
- ><a name="3882"
- > </a
- ><a name="3884" class="Symbol"
- >=</a
><a name="3885"
> </a
- ><a name="3887" href="Maps.html#2188" class="InductiveConstructor"
+ ><a name="3887" class="Symbol"
+ >=</a
+ ><a name="3888"
+ > </a
+ ><a name="3890" href="Maps.html#2188" class="InductiveConstructor"
>id</a
- ><a name="3889"
+ ><a name="3892"
> </a
- ><a name="3890" class="Number"
+ ><a name="3893" class="Number"
>0</a
- ><a name="3891"
+ ><a name="3894"
>
</a
- ><a name="3892" href="Stlc.html#3874" class="Function"
+ ><a name="3895" href="Stlc.html#3877" class="Function"
>x</a
- ><a name="3893"
- > </a
- ><a name="3895" class="Symbol"
- >=</a
><a name="3896"
> </a
- ><a name="3898" href="Maps.html#2188" class="InductiveConstructor"
+ ><a name="3898" class="Symbol"
+ >=</a
+ ><a name="3899"
+ > </a
+ ><a name="3901" href="Maps.html#2188" class="InductiveConstructor"
>id</a
- ><a name="3900"
+ ><a name="3903"
> </a
- ><a name="3901" class="Number"
+ ><a name="3904" class="Number"
>1</a
- ><a name="3902"
+ ><a name="3905"
>
</a
- ><a name="3904" href="Stlc.html#3904" class="Function"
+ ><a name="3907" href="Stlc.html#3907" class="Function"
>not</a
- ><a name="3907"
+ ><a name="3910"
> </a
- ><a name="3908" href="Stlc.html#3908" class="Function"
+ ><a name="3911" href="Stlc.html#3911" class="Function"
>two</a
- ><a name="3911"
+ ><a name="3914"
> </a
- ><a name="3912" class="Symbol"
+ ><a name="3915" class="Symbol"
>:</a
- ><a name="3913"
+ ><a name="3916"
> </a
- ><a name="3914" href="Stlc.html#3482" class="Datatype"
+ ><a name="3917" href="Stlc.html#3485" class="Datatype"
>Term</a
- ><a name="3918"
+ ><a name="3921"
>
</a
- ><a name="3920" href="Stlc.html#3904" class="Function"
+ ><a name="3923" href="Stlc.html#3907" class="Function"
>not</a
- ><a name="3923"
+ ><a name="3926"
> </a
- ><a name="3924" class="Symbol"
+ ><a name="3927" class="Symbol"
>=</a
- ><a name="3925"
+ ><a name="3928"
> </a
- ><a name="3927" href="Stlc.html#3517" class="InductiveConstructor Operator"
+ ><a name="3930" href="Stlc.html#3520" class="InductiveConstructor Operator"
>λ[</a
- ><a name="3929"
+ ><a name="3932"
> </a
- ><a name="3930" href="Stlc.html#3874" class="Function"
+ ><a name="3933" href="Stlc.html#3877" class="Function"
>x</a
- ><a name="3931"
+ ><a name="3934"
> </a
- ><a name="3932" href="Stlc.html#3517" class="InductiveConstructor Operator"
+ ><a name="3935" href="Stlc.html#3520" class="InductiveConstructor Operator"
>∶</a
- ><a name="3933"
+ ><a name="3936"
> </a
- ><a name="3934" href="Stlc.html#2577" class="InductiveConstructor"
+ ><a name="3937" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
- ><a name="3935"
+ ><a name="3938"
> </a
- ><a name="3936" href="Stlc.html#3517" class="InductiveConstructor Operator"
+ ><a name="3939" href="Stlc.html#3520" class="InductiveConstructor Operator"
>]</a
- ><a name="3937"
+ ><a name="3940"
> </a
- ><a name="3938" class="Symbol"
+ ><a name="3941" class="Symbol"
>(</a
- ><a name="3939" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="3942" href="Stlc.html#3612" class="InductiveConstructor Operator"
>if</a
- ><a name="3941"
+ ><a name="3944"
> </a
- ><a name="3942" href="Stlc.html#3501" class="InductiveConstructor"
+ ><a name="3945" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
- ><a name="3943"
+ ><a name="3946"
> </a
- ><a name="3944" href="Stlc.html#3874" class="Function"
+ ><a name="3947" href="Stlc.html#3877" class="Function"
>x</a
- ><a name="3945"
+ ><a name="3948"
> </a
- ><a name="3946" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="3949" href="Stlc.html#3612" class="InductiveConstructor Operator"
>then</a
- ><a name="3950"
+ ><a name="3953"
> </a
- ><a name="3951" href="Stlc.html#3594" class="InductiveConstructor"
+ ><a name="3954" href="Stlc.html#3597" class="InductiveConstructor"
>false</a
- ><a name="3956"
+ ><a name="3959"
> </a
- ><a name="3957" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="3960" href="Stlc.html#3612" class="InductiveConstructor Operator"
>else</a
- ><a name="3961"
+ ><a name="3964"
> </a
- ><a name="3962" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="3965" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="3966" class="Symbol"
+ ><a name="3969" class="Symbol"
>)</a
- ><a name="3967"
+ ><a name="3970"
>
</a
- ><a name="3968" href="Stlc.html#3908" class="Function"
+ ><a name="3971" href="Stlc.html#3911" class="Function"
>two</a
- ><a name="3971"
+ ><a name="3974"
> </a
- ><a name="3972" class="Symbol"
+ ><a name="3975" class="Symbol"
>=</a
- ><a name="3973"
+ ><a name="3976"
> </a
- ><a name="3975" href="Stlc.html#3517" class="InductiveConstructor Operator"
+ ><a name="3978" href="Stlc.html#3520" class="InductiveConstructor Operator"
>λ[</a
- ><a name="3977"
+ ><a name="3980"
> </a
- ><a name="3978" href="Stlc.html#3872" class="Function"
+ ><a name="3981" href="Stlc.html#3875" class="Function"
>f</a
- ><a name="3979"
+ ><a name="3982"
> </a
- ><a name="3980" href="Stlc.html#3517" class="InductiveConstructor Operator"
+ ><a name="3983" href="Stlc.html#3520" class="InductiveConstructor Operator"
>∶</a
- ><a name="3981"
+ ><a name="3984"
> </a
- ><a name="3982" href="Stlc.html#2577" class="InductiveConstructor"
+ ><a name="3985" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
- ><a name="3983"
+ ><a name="3986"
> </a
- ><a name="3984" href="Stlc.html#2550" class="InductiveConstructor Operator"
+ ><a name="3987" href="Stlc.html#2550" class="InductiveConstructor Operator"
>⇒</a
- ><a name="3985"
+ ><a name="3988"
> </a
- ><a name="3986" href="Stlc.html#2577" class="InductiveConstructor"
+ ><a name="3989" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
- ><a name="3987"
+ ><a name="3990"
> </a
- ><a name="3988" href="Stlc.html#3517" class="InductiveConstructor Operator"
+ ><a name="3991" href="Stlc.html#3520" class="InductiveConstructor Operator"
>]</a
- ><a name="3989"
- > </a
- ><a name="3990" href="Stlc.html#3517" class="InductiveConstructor Operator"
- >λ[</a
><a name="3992"
> </a
- ><a name="3993" href="Stlc.html#3874" class="Function"
+ ><a name="3993" href="Stlc.html#3520" class="InductiveConstructor Operator"
+ >λ[</a
+ ><a name="3995"
+ > </a
+ ><a name="3996" href="Stlc.html#3877" class="Function"
>x</a
- ><a name="3994"
+ ><a name="3997"
> </a
- ><a name="3995" href="Stlc.html#3517" class="InductiveConstructor Operator"
+ ><a name="3998" href="Stlc.html#3520" class="InductiveConstructor Operator"
>∶</a
- ><a name="3996"
+ ><a name="3999"
> </a
- ><a name="3997" href="Stlc.html#2577" class="InductiveConstructor"
+ ><a name="4000" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
- ><a name="3998"
+ ><a name="4001"
> </a
- ><a name="3999" href="Stlc.html#3517" class="InductiveConstructor Operator"
+ ><a name="4002" href="Stlc.html#3520" class="InductiveConstructor Operator"
>]</a
- ><a name="4000"
+ ><a name="4003"
> </a
- ><a name="4001" href="Stlc.html#3501" class="InductiveConstructor"
+ ><a name="4004" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
- ><a name="4002"
+ ><a name="4005"
> </a
- ><a name="4003" href="Stlc.html#3872" class="Function"
+ ><a name="4006" href="Stlc.html#3875" class="Function"
>f</a
- ><a name="4004"
+ ><a name="4007"
> </a
- ><a name="4005" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="4008" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
- ><a name="4006"
- > </a
- ><a name="4007" class="Symbol"
- >(</a
- ><a name="4008" href="Stlc.html#3501" class="InductiveConstructor"
- >`</a
><a name="4009"
> </a
- ><a name="4010" href="Stlc.html#3872" class="Function"
- >f</a
- ><a name="4011"
- > </a
- ><a name="4012" href="Stlc.html#3553" class="InductiveConstructor Operator"
- >·</a
- ><a name="4013"
- > </a
- ><a name="4014" href="Stlc.html#3501" class="InductiveConstructor"
+ ><a name="4010" class="Symbol"
+ >(</a
+ ><a name="4011" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
- ><a name="4015"
+ ><a name="4012"
> </a
- ><a name="4016" href="Stlc.html#3874" class="Function"
+ ><a name="4013" href="Stlc.html#3875" class="Function"
+ >f</a
+ ><a name="4014"
+ > </a
+ ><a name="4015" href="Stlc.html#3556" class="InductiveConstructor Operator"
+ >·</a
+ ><a name="4016"
+ > </a
+ ><a name="4017" href="Stlc.html#3504" class="InductiveConstructor"
+ >`</a
+ ><a name="4018"
+ > </a
+ ><a name="4019" href="Stlc.html#3877" class="Function"
>x</a
- ><a name="4017" class="Symbol"
+ ><a name="4020" class="Symbol"
>)</a
>
@@ -841,130 +841,130 @@ Example terms.
<pre class="Agda">
-<a name="4055" class="Keyword"
+<a name="4058" class="Keyword"
>data</a
- ><a name="4059"
+ ><a name="4062"
> </a
- ><a name="4060" href="Stlc.html#4060" class="Datatype"
+ ><a name="4063" href="Stlc.html#4063" class="Datatype"
>Value</a
- ><a name="4065"
+ ><a name="4068"
> </a
- ><a name="4066" class="Symbol"
+ ><a name="4069" class="Symbol"
>:</a
- ><a name="4067"
+ ><a name="4070"
> </a
- ><a name="4068" href="Stlc.html#3482" class="Datatype"
+ ><a name="4071" href="Stlc.html#3485" class="Datatype"
>Term</a
- ><a name="4072"
+ ><a name="4075"
> </a
- ><a name="4073" class="Symbol"
+ ><a name="4076" class="Symbol"
>→</a
- ><a name="4074"
+ ><a name="4077"
> </a
- ><a name="4075" class="PrimitiveType"
+ ><a name="4078" class="PrimitiveType"
>Set</a
- ><a name="4078"
+ ><a name="4081"
> </a
- ><a name="4079" class="Keyword"
+ ><a name="4082" class="Keyword"
>where</a
- ><a name="4084"
+ ><a name="4087"
>
</a
- ><a name="4087" href="Stlc.html#4087" class="InductiveConstructor"
+ ><a name="4090" href="Stlc.html#4090" class="InductiveConstructor"
>value-λ</a
- ><a name="4094"
+ ><a name="4097"
> </a
- ><a name="4099" class="Symbol"
+ ><a name="4102" class="Symbol"
>:</a
- ><a name="4100"
+ ><a name="4103"
> </a
- ><a name="4101" class="Symbol"
+ ><a name="4104" class="Symbol"
>∀</a
- ><a name="4102"
- > </a
- ><a name="4103" class="Symbol"
- >{</a
- ><a name="4104" href="Stlc.html#4104" class="Bound"
- >x</a
><a name="4105"
> </a
- ><a name="4106" href="Stlc.html#4106" class="Bound"
- >A</a
- ><a name="4107"
+ ><a name="4106" class="Symbol"
+ >{</a
+ ><a name="4107" href="Stlc.html#4107" class="Bound"
+ >x</a
+ ><a name="4108"
> </a
- ><a name="4108" href="Stlc.html#4108" class="Bound"
- >N</a
- ><a name="4109" class="Symbol"
- >}</a
+ ><a name="4109" href="Stlc.html#4109" class="Bound"
+ >A</a
><a name="4110"
> </a
- ><a name="4111" class="Symbol"
- >→</a
- ><a name="4112"
- > </a
- ><a name="4113" href="Stlc.html#4060" class="Datatype"
- >Value</a
- ><a name="4118"
- > </a
- ><a name="4119" class="Symbol"
- >(</a
- ><a name="4120" href="Stlc.html#3517" class="InductiveConstructor Operator"
- >λ[</a
- ><a name="4122"
- > </a
- ><a name="4123" href="Stlc.html#4104" class="Bound"
- >x</a
- ><a name="4124"
- > </a
- ><a name="4125" href="Stlc.html#3517" class="InductiveConstructor Operator"
- >∶</a
- ><a name="4126"
- > </a
- ><a name="4127" href="Stlc.html#4106" class="Bound"
- >A</a
- ><a name="4128"
- > </a
- ><a name="4129" href="Stlc.html#3517" class="InductiveConstructor Operator"
- >]</a
- ><a name="4130"
- > </a
- ><a name="4131" href="Stlc.html#4108" class="Bound"
+ ><a name="4111" href="Stlc.html#4111" class="Bound"
>N</a
- ><a name="4132" class="Symbol"
- >)</a
+ ><a name="4112" class="Symbol"
+ >}</a
+ ><a name="4113"
+ > </a
+ ><a name="4114" class="Symbol"
+ >→</a
+ ><a name="4115"
+ > </a
+ ><a name="4116" href="Stlc.html#4063" class="Datatype"
+ >Value</a
+ ><a name="4121"
+ > </a
+ ><a name="4122" class="Symbol"
+ >(</a
+ ><a name="4123" href="Stlc.html#3520" class="InductiveConstructor Operator"
+ >λ[</a
+ ><a name="4125"
+ > </a
+ ><a name="4126" href="Stlc.html#4107" class="Bound"
+ >x</a
+ ><a name="4127"
+ > </a
+ ><a name="4128" href="Stlc.html#3520" class="InductiveConstructor Operator"
+ >∶</a
+ ><a name="4129"
+ > </a
+ ><a name="4130" href="Stlc.html#4109" class="Bound"
+ >A</a
+ ><a name="4131"
+ > </a
+ ><a name="4132" href="Stlc.html#3520" class="InductiveConstructor Operator"
+ >]</a
><a name="4133"
+ > </a
+ ><a name="4134" href="Stlc.html#4111" class="Bound"
+ >N</a
+ ><a name="4135" class="Symbol"
+ >)</a
+ ><a name="4136"
>
</a
- ><a name="4136" href="Stlc.html#4136" class="InductiveConstructor"
+ ><a name="4139" href="Stlc.html#4139" class="InductiveConstructor"
>value-true</a
- ><a name="4146"
- > </a
- ><a name="4148" class="Symbol"
- >:</a
><a name="4149"
+ > </a
+ ><a name="4151" class="Symbol"
+ >:</a
+ ><a name="4152"
> </a
- ><a name="4150" href="Stlc.html#4060" class="Datatype"
+ ><a name="4153" href="Stlc.html#4063" class="Datatype"
>Value</a
- ><a name="4155"
+ ><a name="4158"
> </a
- ><a name="4156" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="4159" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="4160"
+ ><a name="4163"
>
</a
- ><a name="4163" href="Stlc.html#4163" class="InductiveConstructor"
+ ><a name="4166" href="Stlc.html#4166" class="InductiveConstructor"
>value-false</a
- ><a name="4174"
+ ><a name="4177"
> </a
- ><a name="4175" class="Symbol"
+ ><a name="4178" class="Symbol"
>:</a
- ><a name="4176"
+ ><a name="4179"
> </a
- ><a name="4177" href="Stlc.html#4060" class="Datatype"
+ ><a name="4180" href="Stlc.html#4063" class="Datatype"
>Value</a
- ><a name="4182"
+ ><a name="4185"
> </a
- ><a name="4183" href="Stlc.html#3594" class="InductiveConstructor"
+ ><a name="4186" href="Stlc.html#3597" class="InductiveConstructor"
>false</a
>
@@ -974,645 +974,645 @@ Example terms.
<pre class="Agda">
-<a name="4231" href="Stlc.html#4231" class="Function Operator"
+<a name="4234" href="Stlc.html#4234" class="Function Operator"
>_[_:=_]</a
- ><a name="4238"
+ ><a name="4241"
> </a
- ><a name="4239" class="Symbol"
+ ><a name="4242" class="Symbol"
>:</a
- ><a name="4240"
+ ><a name="4243"
> </a
- ><a name="4241" href="Stlc.html#3482" class="Datatype"
+ ><a name="4244" href="Stlc.html#3485" class="Datatype"
>Term</a
- ><a name="4245"
+ ><a name="4248"
> </a
- ><a name="4246" class="Symbol"
+ ><a name="4249" class="Symbol"
>→</a
- ><a name="4247"
- > </a
- ><a name="4248" href="Maps.html#2171" class="Datatype"
- >Id</a
><a name="4250"
> </a
- ><a name="4251" class="Symbol"
+ ><a name="4251" href="Maps.html#2171" class="Datatype"
+ >Id</a
+ ><a name="4253"
+ > </a
+ ><a name="4254" class="Symbol"
>→</a
- ><a name="4252"
+ ><a name="4255"
> </a
- ><a name="4253" href="Stlc.html#3482" class="Datatype"
+ ><a name="4256" href="Stlc.html#3485" class="Datatype"
>Term</a
- ><a name="4257"
+ ><a name="4260"
> </a
- ><a name="4258" class="Symbol"
+ ><a name="4261" class="Symbol"
>→</a
- ><a name="4259"
+ ><a name="4262"
> </a
- ><a name="4260" href="Stlc.html#3482" class="Datatype"
+ ><a name="4263" href="Stlc.html#3485" class="Datatype"
>Term</a
- ><a name="4264"
+ ><a name="4267"
>
</a
- ><a name="4265" class="Symbol"
+ ><a name="4268" class="Symbol"
>(</a
- ><a name="4266" href="Stlc.html#3501" class="InductiveConstructor"
+ ><a name="4269" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
- ><a name="4267"
+ ><a name="4270"
> </a
- ><a name="4268" href="Stlc.html#4268" class="Bound"
+ ><a name="4271" href="Stlc.html#4271" class="Bound"
>x′</a
- ><a name="4270" class="Symbol"
+ ><a name="4273" class="Symbol"
>)</a
- ><a name="4271"
+ ><a name="4274"
> </a
- ><a name="4272" href="Stlc.html#4231" class="Function Operator"
+ ><a name="4275" href="Stlc.html#4234" class="Function Operator"
>[</a
- ><a name="4273"
+ ><a name="4276"
> </a
- ><a name="4274" href="Stlc.html#4274" class="Bound"
+ ><a name="4277" href="Stlc.html#4277" class="Bound"
>x</a
- ><a name="4275"
- > </a
- ><a name="4276" href="Stlc.html#4231" class="Function Operator"
- >:=</a
><a name="4278"
> </a
- ><a name="4279" href="Stlc.html#4279" class="Bound"
- >V</a
- ><a name="4280"
+ ><a name="4279" href="Stlc.html#4234" class="Function Operator"
+ >:=</a
+ ><a name="4281"
> </a
- ><a name="4281" href="Stlc.html#4231" class="Function Operator"
+ ><a name="4282" href="Stlc.html#4282" class="Bound"
+ >V</a
+ ><a name="4283"
+ > </a
+ ><a name="4284" href="Stlc.html#4234" class="Function Operator"
>]</a
- ><a name="4282"
+ ><a name="4285"
> </a
- ><a name="4283" class="Keyword"
+ ><a name="4286" class="Keyword"
>with</a
- ><a name="4287"
+ ><a name="4290"
> </a
- ><a name="4288" href="Stlc.html#4274" class="Bound"
+ ><a name="4291" href="Stlc.html#4277" class="Bound"
>x</a
- ><a name="4289"
+ ><a name="4292"
> </a
- ><a name="4290" href="Maps.html#2509" class="Function Operator"
+ ><a name="4293" href="Maps.html#2509" class="Function Operator"
>≟</a
- ><a name="4291"
- > </a
- ><a name="4292" href="Stlc.html#4268" class="Bound"
- >x′</a
><a name="4294"
+ > </a
+ ><a name="4295" href="Stlc.html#4271" class="Bound"
+ >x′</a
+ ><a name="4297"
>
</a
- ><a name="4295" class="Symbol"
+ ><a name="4298" class="Symbol"
>...</a
- ><a name="4298"
+ ><a name="4301"
> </a
- ><a name="4299" class="Symbol"
+ ><a name="4302" class="Symbol"
>|</a
- ><a name="4300"
+ ><a name="4303"
> </a
- ><a name="4301" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#520" class="InductiveConstructor"
+ ><a name="4304" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#520" class="InductiveConstructor"
>yes</a
- ><a name="4304"
+ ><a name="4307"
> </a
- ><a name="4305" class="Symbol"
+ ><a name="4308" class="Symbol"
>_</a
- ><a name="4306"
+ ><a name="4309"
> </a
- ><a name="4307" class="Symbol"
+ ><a name="4310" class="Symbol"
>=</a
- ><a name="4308"
+ ><a name="4311"
> </a
- ><a name="4309" href="Stlc.html#4279" class="Bound"
+ ><a name="4312" href="Stlc.html#4282" class="Bound"
>V</a
- ><a name="4310"
+ ><a name="4313"
>
</a
- ><a name="4311" class="Symbol"
+ ><a name="4314" class="Symbol"
>...</a
- ><a name="4314"
+ ><a name="4317"
> </a
- ><a name="4315" class="Symbol"
+ ><a name="4318" class="Symbol"
>|</a
- ><a name="4316"
- > </a
- ><a name="4317" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#547" class="InductiveConstructor"
- >no</a
><a name="4319"
- > </a
- ><a name="4321" class="Symbol"
- >_</a
+ > </a
+ ><a name="4320" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#547" class="InductiveConstructor"
+ >no</a
><a name="4322"
+ > </a
+ ><a name="4324" class="Symbol"
+ >_</a
+ ><a name="4325"
> </a
- ><a name="4323" class="Symbol"
+ ><a name="4326" class="Symbol"
>=</a
- ><a name="4324"
+ ><a name="4327"
> </a
- ><a name="4325" href="Stlc.html#3501" class="InductiveConstructor"
+ ><a name="4328" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
- ><a name="4326"
- > </a
- ><a name="4327" href="Stlc.html#4268" class="Bound"
- >x′</a
><a name="4329"
+ > </a
+ ><a name="4330" href="Stlc.html#4271" class="Bound"
+ >x′</a
+ ><a name="4332"
>
</a
- ><a name="4330" class="Symbol"
+ ><a name="4333" class="Symbol"
>(</a
- ><a name="4331" href="Stlc.html#3517" class="InductiveConstructor Operator"
+ ><a name="4334" href="Stlc.html#3520" class="InductiveConstructor Operator"
>λ[</a
- ><a name="4333"
- > </a
- ><a name="4334" href="Stlc.html#4334" class="Bound"
- >x′</a
><a name="4336"
> </a
- ><a name="4337" href="Stlc.html#3517" class="InductiveConstructor Operator"
- >∶</a
- ><a name="4338"
+ ><a name="4337" href="Stlc.html#4337" class="Bound"
+ >x′</a
+ ><a name="4339"
> </a
- ><a name="4339" href="Stlc.html#4339" class="Bound"
- >A′</a
+ ><a name="4340" href="Stlc.html#3520" class="InductiveConstructor Operator"
+ >∶</a
><a name="4341"
> </a
- ><a name="4342" href="Stlc.html#3517" class="InductiveConstructor Operator"
+ ><a name="4342" href="Stlc.html#4342" class="Bound"
+ >A′</a
+ ><a name="4344"
+ > </a
+ ><a name="4345" href="Stlc.html#3520" class="InductiveConstructor Operator"
>]</a
- ><a name="4343"
+ ><a name="4346"
> </a
- ><a name="4344" href="Stlc.html#4344" class="Bound"
+ ><a name="4347" href="Stlc.html#4347" class="Bound"
>N′</a
- ><a name="4346" class="Symbol"
+ ><a name="4349" class="Symbol"
>)</a
- ><a name="4347"
+ ><a name="4350"
> </a
- ><a name="4348" href="Stlc.html#4231" class="Function Operator"
+ ><a name="4351" href="Stlc.html#4234" class="Function Operator"
>[</a
- ><a name="4349"
+ ><a name="4352"
> </a
- ><a name="4350" href="Stlc.html#4350" class="Bound"
+ ><a name="4353" href="Stlc.html#4353" class="Bound"
>x</a
- ><a name="4351"
- > </a
- ><a name="4352" href="Stlc.html#4231" class="Function Operator"
- >:=</a
><a name="4354"
> </a
- ><a name="4355" href="Stlc.html#4355" class="Bound"
+ ><a name="4355" href="Stlc.html#4234" class="Function Operator"
+ >:=</a
+ ><a name="4357"
+ > </a
+ ><a name="4358" href="Stlc.html#4358" class="Bound"
>V</a
- ><a name="4356"
+ ><a name="4359"
> </a
- ><a name="4357" href="Stlc.html#4231" class="Function Operator"
+ ><a name="4360" href="Stlc.html#4234" class="Function Operator"
>]</a
- ><a name="4358"
+ ><a name="4361"
> </a
- ><a name="4359" class="Keyword"
+ ><a name="4362" class="Keyword"
>with</a
- ><a name="4363"
+ ><a name="4366"
> </a
- ><a name="4364" href="Stlc.html#4350" class="Bound"
+ ><a name="4367" href="Stlc.html#4353" class="Bound"
>x</a
- ><a name="4365"
+ ><a name="4368"
> </a
- ><a name="4366" href="Maps.html#2509" class="Function Operator"
+ ><a name="4369" href="Maps.html#2509" class="Function Operator"
>≟</a
- ><a name="4367"
- > </a
- ><a name="4368" href="Stlc.html#4334" class="Bound"
- >x′</a
><a name="4370"
+ > </a
+ ><a name="4371" href="Stlc.html#4337" class="Bound"
+ >x′</a
+ ><a name="4373"
>
</a
- ><a name="4371" class="Symbol"
+ ><a name="4374" class="Symbol"
>...</a
- ><a name="4374"
+ ><a name="4377"
> </a
- ><a name="4375" class="Symbol"
+ ><a name="4378" class="Symbol"
>|</a
- ><a name="4376"
+ ><a name="4379"
> </a
- ><a name="4377" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#520" class="InductiveConstructor"
+ ><a name="4380" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#520" class="InductiveConstructor"
>yes</a
- ><a name="4380"
+ ><a name="4383"
> </a
- ><a name="4381" class="Symbol"
+ ><a name="4384" class="Symbol"
>_</a
- ><a name="4382"
+ ><a name="4385"
> </a
- ><a name="4383" class="Symbol"
+ ><a name="4386" class="Symbol"
>=</a
- ><a name="4384"
- > </a
- ><a name="4385" href="Stlc.html#3517" class="InductiveConstructor Operator"
- >λ[</a
><a name="4387"
> </a
- ><a name="4388" href="Stlc.html#4334" class="Bound"
- >x′</a
+ ><a name="4388" href="Stlc.html#3520" class="InductiveConstructor Operator"
+ >λ[</a
><a name="4390"
> </a
- ><a name="4391" href="Stlc.html#3517" class="InductiveConstructor Operator"
- >∶</a
- ><a name="4392"
+ ><a name="4391" href="Stlc.html#4337" class="Bound"
+ >x′</a
+ ><a name="4393"
> </a
- ><a name="4393" href="Stlc.html#4339" class="Bound"
- >A′</a
+ ><a name="4394" href="Stlc.html#3520" class="InductiveConstructor Operator"
+ >∶</a
><a name="4395"
> </a
- ><a name="4396" href="Stlc.html#3517" class="InductiveConstructor Operator"
- >]</a
- ><a name="4397"
+ ><a name="4396" href="Stlc.html#4342" class="Bound"
+ >A′</a
+ ><a name="4398"
> </a
- ><a name="4398" href="Stlc.html#4344" class="Bound"
- >N′</a
+ ><a name="4399" href="Stlc.html#3520" class="InductiveConstructor Operator"
+ >]</a
><a name="4400"
+ > </a
+ ><a name="4401" href="Stlc.html#4347" class="Bound"
+ >N′</a
+ ><a name="4403"
>
</a
- ><a name="4401" class="Symbol"
+ ><a name="4404" class="Symbol"
>...</a
- ><a name="4404"
+ ><a name="4407"
> </a
- ><a name="4405" class="Symbol"
+ ><a name="4408" class="Symbol"
>|</a
- ><a name="4406"
- > </a
- ><a name="4407" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#547" class="InductiveConstructor"
- >no</a
><a name="4409"
- > </a
- ><a name="4411" class="Symbol"
- >_</a
+ > </a
+ ><a name="4410" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#547" class="InductiveConstructor"
+ >no</a
><a name="4412"
+ > </a
+ ><a name="4414" class="Symbol"
+ >_</a
+ ><a name="4415"
> </a
- ><a name="4413" class="Symbol"
+ ><a name="4416" class="Symbol"
>=</a
- ><a name="4414"
- > </a
- ><a name="4415" href="Stlc.html#3517" class="InductiveConstructor Operator"
- >λ[</a
><a name="4417"
> </a
- ><a name="4418" href="Stlc.html#4334" class="Bound"
- >x′</a
+ ><a name="4418" href="Stlc.html#3520" class="InductiveConstructor Operator"
+ >λ[</a
><a name="4420"
> </a
- ><a name="4421" href="Stlc.html#3517" class="InductiveConstructor Operator"
- >∶</a
- ><a name="4422"
+ ><a name="4421" href="Stlc.html#4337" class="Bound"
+ >x′</a
+ ><a name="4423"
> </a
- ><a name="4423" href="Stlc.html#4339" class="Bound"
- >A′</a
+ ><a name="4424" href="Stlc.html#3520" class="InductiveConstructor Operator"
+ >∶</a
><a name="4425"
> </a
- ><a name="4426" href="Stlc.html#3517" class="InductiveConstructor Operator"
+ ><a name="4426" href="Stlc.html#4342" class="Bound"
+ >A′</a
+ ><a name="4428"
+ > </a
+ ><a name="4429" href="Stlc.html#3520" class="InductiveConstructor Operator"
>]</a
- ><a name="4427"
+ ><a name="4430"
> </a
- ><a name="4428" class="Symbol"
+ ><a name="4431" class="Symbol"
>(</a
- ><a name="4429" href="Stlc.html#4344" class="Bound"
+ ><a name="4432" href="Stlc.html#4347" class="Bound"
>N′</a
- ><a name="4431"
+ ><a name="4434"
> </a
- ><a name="4432" href="Stlc.html#4231" class="Function Operator"
+ ><a name="4435" href="Stlc.html#4234" class="Function Operator"
>[</a
- ><a name="4433"
+ ><a name="4436"
> </a
- ><a name="4434" href="Stlc.html#4350" class="Bound"
+ ><a name="4437" href="Stlc.html#4353" class="Bound"
>x</a
- ><a name="4435"
- > </a
- ><a name="4436" href="Stlc.html#4231" class="Function Operator"
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><a name="4438"
> </a
- ><a name="4439" href="Stlc.html#4355" class="Bound"
- >V</a
- ><a name="4440"
+ ><a name="4439" href="Stlc.html#4234" class="Function Operator"
+ >:=</a
+ ><a name="4441"
> </a
- ><a name="4441" href="Stlc.html#4231" class="Function Operator"
- >]</a
- ><a name="4442" class="Symbol"
- >)</a
+ ><a name="4442" href="Stlc.html#4358" class="Bound"
+ >V</a
><a name="4443"
+ > </a
+ ><a name="4444" href="Stlc.html#4234" class="Function Operator"
+ >]</a
+ ><a name="4445" class="Symbol"
+ >)</a
+ ><a name="4446"
>
</a
- ><a name="4444" class="Symbol"
+ ><a name="4447" class="Symbol"
>(</a
- ><a name="4445" href="Stlc.html#4445" class="Bound"
+ ><a name="4448" href="Stlc.html#4448" class="Bound"
>L′</a
- ><a name="4447"
+ ><a name="4450"
> </a
- ><a name="4448" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="4451" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
- ><a name="4449"
+ ><a name="4452"
> </a
- ><a name="4450" href="Stlc.html#4450" class="Bound"
+ ><a name="4453" href="Stlc.html#4453" class="Bound"
>M′</a
- ><a name="4452" class="Symbol"
+ ><a name="4455" class="Symbol"
>)</a
- ><a name="4453"
+ ><a name="4456"
> </a
- ><a name="4454" href="Stlc.html#4231" class="Function Operator"
+ ><a name="4457" href="Stlc.html#4234" class="Function Operator"
>[</a
- ><a name="4455"
+ ><a name="4458"
> </a
- ><a name="4456" href="Stlc.html#4456" class="Bound"
+ ><a name="4459" href="Stlc.html#4459" class="Bound"
>x</a
- ><a name="4457"
- > </a
- ><a name="4458" href="Stlc.html#4231" class="Function Operator"
- >:=</a
><a name="4460"
> </a
- ><a name="4461" href="Stlc.html#4461" class="Bound"
- >V</a
- ><a name="4462"
- > </a
- ><a name="4463" href="Stlc.html#4231" class="Function Operator"
- >]</a
- ><a name="4464"
- > </a
- ><a name="4465" class="Symbol"
- >=</a
- ><a name="4466"
- > </a
- ><a name="4468" class="Symbol"
- >(</a
- ><a name="4469" href="Stlc.html#4445" class="Bound"
- >L′</a
- ><a name="4471"
- > </a
- ><a name="4472" href="Stlc.html#4231" class="Function Operator"
- >[</a
- ><a name="4473"
- > </a
- ><a name="4474" href="Stlc.html#4456" class="Bound"
- >x</a
- ><a name="4475"
- > </a
- ><a name="4476" href="Stlc.html#4231" class="Function Operator"
+ ><a name="4461" href="Stlc.html#4234" class="Function Operator"
>:=</a
+ ><a name="4463"
+ > </a
+ ><a name="4464" href="Stlc.html#4464" class="Bound"
+ >V</a
+ ><a name="4465"
+ > </a
+ ><a name="4466" href="Stlc.html#4234" class="Function Operator"
+ >]</a
+ ><a name="4467"
+ > </a
+ ><a name="4468" class="Symbol"
+ >=</a
+ ><a name="4469"
+ > </a
+ ><a name="4471" class="Symbol"
+ >(</a
+ ><a name="4472" href="Stlc.html#4448" class="Bound"
+ >L′</a
+ ><a name="4474"
+ > </a
+ ><a name="4475" href="Stlc.html#4234" class="Function Operator"
+ >[</a
+ ><a name="4476"
+ > </a
+ ><a name="4477" href="Stlc.html#4459" class="Bound"
+ >x</a
><a name="4478"
> </a
- ><a name="4479" href="Stlc.html#4461" class="Bound"
- >V</a
- ><a name="4480"
+ ><a name="4479" href="Stlc.html#4234" class="Function Operator"
+ >:=</a
+ ><a name="4481"
> </a
- ><a name="4481" href="Stlc.html#4231" class="Function Operator"
- >]</a
- ><a name="4482" class="Symbol"
- >)</a
+ ><a name="4482" href="Stlc.html#4464" class="Bound"
+ >V</a
><a name="4483"
> </a
- ><a name="4484" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="4484" href="Stlc.html#4234" class="Function Operator"
+ >]</a
+ ><a name="4485" class="Symbol"
+ >)</a
+ ><a name="4486"
+ > </a
+ ><a name="4487" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
- ><a name="4485"
+ ><a name="4488"
> </a
- ><a name="4486" class="Symbol"
+ ><a name="4489" class="Symbol"
>(</a
- ><a name="4487" href="Stlc.html#4450" class="Bound"
+ ><a name="4490" href="Stlc.html#4453" class="Bound"
>M′</a
- ><a name="4489"
+ ><a name="4492"
> </a
- ><a name="4490" href="Stlc.html#4231" class="Function Operator"
+ ><a name="4493" href="Stlc.html#4234" class="Function Operator"
>[</a
- ><a name="4491"
+ ><a name="4494"
> </a
- ><a name="4492" href="Stlc.html#4456" class="Bound"
+ ><a name="4495" href="Stlc.html#4459" class="Bound"
>x</a
- ><a name="4493"
- > </a
- ><a name="4494" href="Stlc.html#4231" class="Function Operator"
- >:=</a
><a name="4496"
> </a
- ><a name="4497" href="Stlc.html#4461" class="Bound"
- >V</a
- ><a name="4498"
+ ><a name="4497" href="Stlc.html#4234" class="Function Operator"
+ >:=</a
+ ><a name="4499"
> </a
- ><a name="4499" href="Stlc.html#4231" class="Function Operator"
- >]</a
- ><a name="4500" class="Symbol"
- >)</a
+ ><a name="4500" href="Stlc.html#4464" class="Bound"
+ >V</a
><a name="4501"
+ > </a
+ ><a name="4502" href="Stlc.html#4234" class="Function Operator"
+ >]</a
+ ><a name="4503" class="Symbol"
+ >)</a
+ ><a name="4504"
>
</a
- ><a name="4502" class="Symbol"
+ ><a name="4505" class="Symbol"
>(</a
- ><a name="4503" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="4506" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="4507" class="Symbol"
+ ><a name="4510" class="Symbol"
>)</a
- ><a name="4508"
+ ><a name="4511"
> </a
- ><a name="4509" href="Stlc.html#4231" class="Function Operator"
+ ><a name="4512" href="Stlc.html#4234" class="Function Operator"
>[</a
- ><a name="4510"
+ ><a name="4513"
> </a
- ><a name="4511" href="Stlc.html#4511" class="Bound"
+ ><a name="4514" href="Stlc.html#4514" class="Bound"
>x</a
- ><a name="4512"
- > </a
- ><a name="4513" href="Stlc.html#4231" class="Function Operator"
- >:=</a
><a name="4515"
> </a
- ><a name="4516" href="Stlc.html#4516" class="Bound"
+ ><a name="4516" href="Stlc.html#4234" class="Function Operator"
+ >:=</a
+ ><a name="4518"
+ > </a
+ ><a name="4519" href="Stlc.html#4519" class="Bound"
>V</a
- ><a name="4517"
+ ><a name="4520"
> </a
- ><a name="4518" href="Stlc.html#4231" class="Function Operator"
+ ><a name="4521" href="Stlc.html#4234" class="Function Operator"
>]</a
- ><a name="4519"
+ ><a name="4522"
> </a
- ><a name="4520" class="Symbol"
+ ><a name="4523" class="Symbol"
>=</a
- ><a name="4521"
+ ><a name="4524"
> </a
- ><a name="4522" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="4525" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="4526"
+ ><a name="4529"
>
</a
- ><a name="4527" class="Symbol"
+ ><a name="4530" class="Symbol"
>(</a
- ><a name="4528" href="Stlc.html#3594" class="InductiveConstructor"
+ ><a name="4531" href="Stlc.html#3597" class="InductiveConstructor"
>false</a
- ><a name="4533" class="Symbol"
+ ><a name="4536" class="Symbol"
>)</a
- ><a name="4534"
+ ><a name="4537"
> </a
- ><a name="4535" href="Stlc.html#4231" class="Function Operator"
+ ><a name="4538" href="Stlc.html#4234" class="Function Operator"
>[</a
- ><a name="4536"
+ ><a name="4539"
> </a
- ><a name="4537" href="Stlc.html#4537" class="Bound"
+ ><a name="4540" href="Stlc.html#4540" class="Bound"
>x</a
- ><a name="4538"
- > </a
- ><a name="4539" href="Stlc.html#4231" class="Function Operator"
- >:=</a
><a name="4541"
> </a
- ><a name="4542" href="Stlc.html#4542" class="Bound"
+ ><a name="4542" href="Stlc.html#4234" class="Function Operator"
+ >:=</a
+ ><a name="4544"
+ > </a
+ ><a name="4545" href="Stlc.html#4545" class="Bound"
>V</a
- ><a name="4543"
+ ><a name="4546"
> </a
- ><a name="4544" href="Stlc.html#4231" class="Function Operator"
+ ><a name="4547" href="Stlc.html#4234" class="Function Operator"
>]</a
- ><a name="4545"
+ ><a name="4548"
> </a
- ><a name="4546" class="Symbol"
+ ><a name="4549" class="Symbol"
>=</a
- ><a name="4547"
+ ><a name="4550"
> </a
- ><a name="4548" href="Stlc.html#3594" class="InductiveConstructor"
+ ><a name="4551" href="Stlc.html#3597" class="InductiveConstructor"
>false</a
- ><a name="4553"
+ ><a name="4556"
>
</a
- ><a name="4554" class="Symbol"
+ ><a name="4557" class="Symbol"
>(</a
- ><a name="4555" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="4558" href="Stlc.html#3612" class="InductiveConstructor Operator"
>if</a
- ><a name="4557"
- > </a
- ><a name="4558" href="Stlc.html#4558" class="Bound"
- >L′</a
><a name="4560"
> </a
- ><a name="4561" href="Stlc.html#3609" class="InductiveConstructor Operator"
- >then</a
- ><a name="4565"
+ ><a name="4561" href="Stlc.html#4561" class="Bound"
+ >L′</a
+ ><a name="4563"
> </a
- ><a name="4566" href="Stlc.html#4566" class="Bound"
- >M′</a
+ ><a name="4564" href="Stlc.html#3612" class="InductiveConstructor Operator"
+ >then</a
><a name="4568"
> </a
- ><a name="4569" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="4569" href="Stlc.html#4569" class="Bound"
+ >M′</a
+ ><a name="4571"
+ > </a
+ ><a name="4572" href="Stlc.html#3612" class="InductiveConstructor Operator"
>else</a
- ><a name="4573"
+ ><a name="4576"
> </a
- ><a name="4574" href="Stlc.html#4574" class="Bound"
+ ><a name="4577" href="Stlc.html#4577" class="Bound"
>N′</a
- ><a name="4576" class="Symbol"
+ ><a name="4579" class="Symbol"
>)</a
- ><a name="4577"
+ ><a name="4580"
> </a
- ><a name="4578" href="Stlc.html#4231" class="Function Operator"
+ ><a name="4581" href="Stlc.html#4234" class="Function Operator"
>[</a
- ><a name="4579"
+ ><a name="4582"
> </a
- ><a name="4580" href="Stlc.html#4580" class="Bound"
+ ><a name="4583" href="Stlc.html#4583" class="Bound"
>x</a
- ><a name="4581"
- > </a
- ><a name="4582" href="Stlc.html#4231" class="Function Operator"
- >:=</a
><a name="4584"
> </a
- ><a name="4585" href="Stlc.html#4585" class="Bound"
+ ><a name="4585" href="Stlc.html#4234" class="Function Operator"
+ >:=</a
+ ><a name="4587"
+ > </a
+ ><a name="4588" href="Stlc.html#4588" class="Bound"
>V</a
- ><a name="4586"
+ ><a name="4589"
> </a
- ><a name="4587" href="Stlc.html#4231" class="Function Operator"
+ ><a name="4590" href="Stlc.html#4234" class="Function Operator"
>]</a
- ><a name="4588"
+ ><a name="4591"
> </a
- ><a name="4589" class="Symbol"
+ ><a name="4592" class="Symbol"
>=</a
- ><a name="4590"
- > </a
- ><a name="4591" href="Stlc.html#3609" class="InductiveConstructor Operator"
- >if</a
><a name="4593"
> </a
- ><a name="4594" class="Symbol"
+ ><a name="4594" href="Stlc.html#3612" class="InductiveConstructor Operator"
+ >if</a
+ ><a name="4596"
+ > </a
+ ><a name="4597" class="Symbol"
>(</a
- ><a name="4595" href="Stlc.html#4558" class="Bound"
+ ><a name="4598" href="Stlc.html#4561" class="Bound"
>L′</a
- ><a name="4597"
+ ><a name="4600"
> </a
- ><a name="4598" href="Stlc.html#4231" class="Function Operator"
+ ><a name="4601" href="Stlc.html#4234" class="Function Operator"
>[</a
- ><a name="4599"
+ ><a name="4602"
> </a
- ><a name="4600" href="Stlc.html#4580" class="Bound"
+ ><a name="4603" href="Stlc.html#4583" class="Bound"
>x</a
- ><a name="4601"
- > </a
- ><a name="4602" href="Stlc.html#4231" class="Function Operator"
- >:=</a
><a name="4604"
> </a
- ><a name="4605" href="Stlc.html#4585" class="Bound"
- >V</a
- ><a name="4606"
+ ><a name="4605" href="Stlc.html#4234" class="Function Operator"
+ >:=</a
+ ><a name="4607"
> </a
- ><a name="4607" href="Stlc.html#4231" class="Function Operator"
- >]</a
- ><a name="4608" class="Symbol"
- >)</a
+ ><a name="4608" href="Stlc.html#4588" class="Bound"
+ >V</a
><a name="4609"
> </a
- ><a name="4610" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="4610" href="Stlc.html#4234" class="Function Operator"
+ >]</a
+ ><a name="4611" class="Symbol"
+ >)</a
+ ><a name="4612"
+ > </a
+ ><a name="4613" href="Stlc.html#3612" class="InductiveConstructor Operator"
>then</a
- ><a name="4614"
+ ><a name="4617"
> </a
- ><a name="4615" class="Symbol"
+ ><a name="4618" class="Symbol"
>(</a
- ><a name="4616" href="Stlc.html#4566" class="Bound"
+ ><a name="4619" href="Stlc.html#4569" class="Bound"
>M′</a
- ><a name="4618"
+ ><a name="4621"
> </a
- ><a name="4619" href="Stlc.html#4231" class="Function Operator"
+ ><a name="4622" href="Stlc.html#4234" class="Function Operator"
>[</a
- ><a name="4620"
+ ><a name="4623"
> </a
- ><a name="4621" href="Stlc.html#4580" class="Bound"
+ ><a name="4624" href="Stlc.html#4583" class="Bound"
>x</a
- ><a name="4622"
- > </a
- ><a name="4623" href="Stlc.html#4231" class="Function Operator"
- >:=</a
><a name="4625"
> </a
- ><a name="4626" href="Stlc.html#4585" class="Bound"
- >V</a
- ><a name="4627"
+ ><a name="4626" href="Stlc.html#4234" class="Function Operator"
+ >:=</a
+ ><a name="4628"
> </a
- ><a name="4628" href="Stlc.html#4231" class="Function Operator"
- >]</a
- ><a name="4629" class="Symbol"
- >)</a
+ ><a name="4629" href="Stlc.html#4588" class="Bound"
+ >V</a
><a name="4630"
> </a
- ><a name="4631" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="4631" href="Stlc.html#4234" class="Function Operator"
+ >]</a
+ ><a name="4632" class="Symbol"
+ >)</a
+ ><a name="4633"
+ > </a
+ ><a name="4634" href="Stlc.html#3612" class="InductiveConstructor Operator"
>else</a
- ><a name="4635"
+ ><a name="4638"
> </a
- ><a name="4636" class="Symbol"
+ ><a name="4639" class="Symbol"
>(</a
- ><a name="4637" href="Stlc.html#4574" class="Bound"
+ ><a name="4640" href="Stlc.html#4577" class="Bound"
>N′</a
- ><a name="4639"
+ ><a name="4642"
> </a
- ><a name="4640" href="Stlc.html#4231" class="Function Operator"
+ ><a name="4643" href="Stlc.html#4234" class="Function Operator"
>[</a
- ><a name="4641"
+ ><a name="4644"
> </a
- ><a name="4642" href="Stlc.html#4580" class="Bound"
+ ><a name="4645" href="Stlc.html#4583" class="Bound"
>x</a
- ><a name="4643"
- > </a
- ><a name="4644" href="Stlc.html#4231" class="Function Operator"
- >:=</a
><a name="4646"
> </a
- ><a name="4647" href="Stlc.html#4585" class="Bound"
- >V</a
- ><a name="4648"
+ ><a name="4647" href="Stlc.html#4234" class="Function Operator"
+ >:=</a
+ ><a name="4649"
> </a
- ><a name="4649" href="Stlc.html#4231" class="Function Operator"
+ ><a name="4650" href="Stlc.html#4588" class="Bound"
+ >V</a
+ ><a name="4651"
+ > </a
+ ><a name="4652" href="Stlc.html#4234" class="Function Operator"
>]</a
- ><a name="4650" class="Symbol"
+ ><a name="4653" class="Symbol"
>)</a
>
@@ -1622,569 +1622,569 @@ Example terms.
<pre class="Agda">
-<a name="4697" class="Keyword"
+<a name="4700" class="Keyword"
>infix</a
- ><a name="4702"
- > </a
- ><a name="4703" class="Number"
- >10</a
><a name="4705"
> </a
- ><a name="4706" href="Stlc.html#4717" class="Datatype Operator"
+ ><a name="4706" class="Number"
+ >10</a
+ ><a name="4708"
+ > </a
+ ><a name="4709" href="Stlc.html#4720" class="Datatype Operator"
>_⟹_</a
- ><a name="4709"
+ ><a name="4712"
>
</a
- ><a name="4712" class="Keyword"
+ ><a name="4715" class="Keyword"
>data</a
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> </a
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>_⟹_</a
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+ ><a name="4723"
> </a
- ><a name="4721" class="Symbol"
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>:</a
- ><a name="4722"
+ ><a name="4725"
> </a
- ><a name="4723" href="Stlc.html#3482" class="Datatype"
+ ><a name="4726" href="Stlc.html#3485" class="Datatype"
>Term</a
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+ ><a name="4730"
> </a
- ><a name="4728" class="Symbol"
+ ><a name="4731" class="Symbol"
>→</a
- ><a name="4729"
+ ><a name="4732"
> </a
- ><a name="4730" href="Stlc.html#3482" class="Datatype"
+ ><a name="4733" href="Stlc.html#3485" class="Datatype"
>Term</a
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> </a
- ><a name="4735" class="Symbol"
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>→</a
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+ ><a name="4739"
> </a
- ><a name="4737" class="PrimitiveType"
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> </a
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>where</a
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+ ><a name="4749"
>
</a
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+ ><a name="4752" href="Stlc.html#4752" class="InductiveConstructor"
>βλ·</a
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+ ><a name="4755"
> </a
- ><a name="4753" class="Symbol"
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>:</a
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> </a
- ><a name="4755" class="Symbol"
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>∀</a
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- >x</a
><a name="4759"
> </a
- ><a name="4760" href="Stlc.html#4760" class="Bound"
+ ><a name="4760" class="Symbol"
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- ><a name="4761"
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> </a
- ><a name="4762" href="Stlc.html#4762" class="Bound"
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>N</a
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- ><a name="4765" class="Symbol"
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><a name="4766"
> </a
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- >Value</a
- ><a name="4774"
- > </a
- ><a name="4775" href="Stlc.html#4764" class="Bound"
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>V</a
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> </a
- ><a name="4777" class="Symbol"
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>→</a
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+ > </a
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+ ><a name="4778" href="Stlc.html#4767" class="Bound"
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>
</a
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>(</a
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>λ[</a
- ><a name="4786"
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> </a
- ><a name="4787" href="Stlc.html#4758" class="Bound"
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>x</a
- ><a name="4788"
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> </a
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>∶</a
- ><a name="4790"
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> </a
- ><a name="4791" href="Stlc.html#4760" class="Bound"
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>A</a
- ><a name="4792"
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> </a
- ><a name="4793" href="Stlc.html#3517" class="InductiveConstructor Operator"
+ ><a name="4796" href="Stlc.html#3520" class="InductiveConstructor Operator"
>]</a
- ><a name="4794"
- > </a
- ><a name="4795" href="Stlc.html#4762" class="Bound"
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><a name="4797"
> </a
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- ><a name="4799"
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- ><a name="4800" href="Stlc.html#4764" class="Bound"
- >V</a
- ><a name="4801"
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- ><a name="4802" href="Stlc.html#4717" class="Datatype Operator"
- >⟹</a
- ><a name="4803"
- > </a
- ><a name="4804" href="Stlc.html#4762" class="Bound"
+ ><a name="4798" href="Stlc.html#4765" class="Bound"
>N</a
- ><a name="4805"
+ ><a name="4799" class="Symbol"
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+ ><a name="4800"
> </a
- ><a name="4806" href="Stlc.html#4231" class="Function Operator"
+ ><a name="4801" href="Stlc.html#3556" class="InductiveConstructor Operator"
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+ ><a name="4802"
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+ ><a name="4803" href="Stlc.html#4767" class="Bound"
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+ ><a name="4804"
+ > </a
+ ><a name="4805" href="Stlc.html#4720" class="Datatype Operator"
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+ ><a name="4806"
+ > </a
+ ><a name="4807" href="Stlc.html#4765" class="Bound"
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>[</a
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+ ><a name="4810"
> </a
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>x</a
- ><a name="4809"
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><a name="4812"
> </a
- ><a name="4813" href="Stlc.html#4764" class="Bound"
- >V</a
- ><a name="4814"
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> </a
- ><a name="4815" href="Stlc.html#4231" class="Function Operator"
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>]</a
- ><a name="4816"
+ ><a name="4819"
>
</a
- ><a name="4819" href="Stlc.html#4819" class="InductiveConstructor"
+ ><a name="4822" href="Stlc.html#4822" class="InductiveConstructor"
>ξ·₁</a
- ><a name="4822"
+ ><a name="4825"
> </a
- ><a name="4823" class="Symbol"
+ ><a name="4826" class="Symbol"
>:</a
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> </a
- ><a name="4825" class="Symbol"
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>∀</a
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- >L</a
><a name="4829"
> </a
- ><a name="4830" href="Stlc.html#4830" class="Bound"
- >L′</a
+ ><a name="4830" class="Symbol"
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+ ><a name="4831" href="Stlc.html#4831" class="Bound"
+ >L</a
><a name="4832"
> </a
><a name="4833" href="Stlc.html#4833" class="Bound"
- >M</a
- ><a name="4834" class="Symbol"
- >}</a
+ >L′</a
><a name="4835"
> </a
- ><a name="4836" class="Symbol"
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>→</a
- ><a name="4837"
+ ><a name="4840"
>
</a
- ><a name="4842" href="Stlc.html#4828" class="Bound"
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>L</a
- ><a name="4843"
+ ><a name="4846"
> </a
- ><a name="4844" href="Stlc.html#4717" class="Datatype Operator"
+ ><a name="4847" href="Stlc.html#4720" class="Datatype Operator"
>⟹</a
- ><a name="4845"
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- ><a name="4846" href="Stlc.html#4830" class="Bound"
- >L′</a
><a name="4848"
> </a
- ><a name="4849" class="Symbol"
+ ><a name="4849" href="Stlc.html#4833" class="Bound"
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+ ><a name="4851"
+ > </a
+ ><a name="4852" class="Symbol"
>→</a
- ><a name="4850"
+ ><a name="4853"
>
</a
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>L</a
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> </a
- ><a name="4857" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="4860" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
- ><a name="4858"
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> </a
- ><a name="4859" href="Stlc.html#4833" class="Bound"
+ ><a name="4862" href="Stlc.html#4836" class="Bound"
>M</a
- ><a name="4860"
+ ><a name="4863"
> </a
- ><a name="4861" href="Stlc.html#4717" class="Datatype Operator"
+ ><a name="4864" href="Stlc.html#4720" class="Datatype Operator"
>⟹</a
- ><a name="4862"
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- ><a name="4863" href="Stlc.html#4830" class="Bound"
- >L′</a
><a name="4865"
> </a
- ><a name="4866" href="Stlc.html#3553" class="InductiveConstructor Operator"
- >·</a
- ><a name="4867"
+ ><a name="4866" href="Stlc.html#4833" class="Bound"
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+ ><a name="4868"
> </a
- ><a name="4868" href="Stlc.html#4833" class="Bound"
+ ><a name="4869" href="Stlc.html#3556" class="InductiveConstructor Operator"
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+ ><a name="4870"
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+ ><a name="4871" href="Stlc.html#4836" class="Bound"
>M</a
- ><a name="4869"
+ ><a name="4872"
>
</a
- ><a name="4872" href="Stlc.html#4872" class="InductiveConstructor"
+ ><a name="4875" href="Stlc.html#4875" class="InductiveConstructor"
>ξ·₂</a
- ><a name="4875"
+ ><a name="4878"
> </a
- ><a name="4876" class="Symbol"
+ ><a name="4879" class="Symbol"
>:</a
- ><a name="4877"
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> </a
- ><a name="4878" class="Symbol"
+ ><a name="4881" class="Symbol"
>∀</a
- ><a name="4879"
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- ><a name="4880" class="Symbol"
- >{</a
- ><a name="4881" href="Stlc.html#4881" class="Bound"
- >V</a
><a name="4882"
> </a
- ><a name="4883" href="Stlc.html#4883" class="Bound"
- >M</a
- ><a name="4884"
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- ><a name="4885" href="Stlc.html#4885" class="Bound"
- >M′</a
- ><a name="4887" class="Symbol"
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- ><a name="4888"
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- ><a name="4889" class="Symbol"
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- ><a name="4890"
- >
- </a
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- >Value</a
- ><a name="4900"
- > </a
- ><a name="4901" href="Stlc.html#4881" class="Bound"
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+ ><a name="4884" href="Stlc.html#4884" class="Bound"
>V</a
- ><a name="4902"
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> </a
- ><a name="4903" class="Symbol"
+ ><a name="4886" href="Stlc.html#4886" class="Bound"
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+ ><a name="4887"
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+ ><a name="4888" href="Stlc.html#4888" class="Bound"
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+ ><a name="4891"
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+ ><a name="4892" class="Symbol"
>→</a
- ><a name="4904"
+ ><a name="4893"
>
</a
- ><a name="4909" href="Stlc.html#4883" class="Bound"
+ ><a name="4898" href="Stlc.html#4063" class="Datatype"
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+ ><a name="4904" href="Stlc.html#4884" class="Bound"
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+ ><a name="4906" class="Symbol"
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+ >
+ </a
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>M</a
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+ ><a name="4913"
> </a
- ><a name="4911" href="Stlc.html#4717" class="Datatype Operator"
+ ><a name="4914" href="Stlc.html#4720" class="Datatype Operator"
>⟹</a
- ><a name="4912"
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- ><a name="4913" href="Stlc.html#4885" class="Bound"
- >M′</a
><a name="4915"
> </a
- ><a name="4916" class="Symbol"
+ ><a name="4916" href="Stlc.html#4888" class="Bound"
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+ ><a name="4919" class="Symbol"
>→</a
- ><a name="4917"
+ ><a name="4920"
>
</a
- ><a name="4922" href="Stlc.html#4881" class="Bound"
+ ><a name="4925" href="Stlc.html#4884" class="Bound"
>V</a
- ><a name="4923"
+ ><a name="4926"
> </a
- ><a name="4924" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="4927" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
- ><a name="4925"
+ ><a name="4928"
> </a
- ><a name="4926" href="Stlc.html#4883" class="Bound"
+ ><a name="4929" href="Stlc.html#4886" class="Bound"
>M</a
- ><a name="4927"
+ ><a name="4930"
> </a
- ><a name="4928" href="Stlc.html#4717" class="Datatype Operator"
+ ><a name="4931" href="Stlc.html#4720" class="Datatype Operator"
>⟹</a
- ><a name="4929"
+ ><a name="4932"
> </a
- ><a name="4930" href="Stlc.html#4881" class="Bound"
+ ><a name="4933" href="Stlc.html#4884" class="Bound"
>V</a
- ><a name="4931"
+ ><a name="4934"
> </a
- ><a name="4932" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="4935" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
- ><a name="4933"
- > </a
- ><a name="4934" href="Stlc.html#4885" class="Bound"
- >M′</a
><a name="4936"
+ > </a
+ ><a name="4937" href="Stlc.html#4888" class="Bound"
+ >M′</a
+ ><a name="4939"
>
</a
- ><a name="4939" href="Stlc.html#4939" class="InductiveConstructor"
+ ><a name="4942" href="Stlc.html#4942" class="InductiveConstructor"
>βif-true</a
- ><a name="4947"
+ ><a name="4950"
> </a
- ><a name="4948" class="Symbol"
+ ><a name="4951" class="Symbol"
>:</a
- ><a name="4949"
+ ><a name="4952"
> </a
- ><a name="4950" class="Symbol"
+ ><a name="4953" class="Symbol"
>∀</a
- ><a name="4951"
- > </a
- ><a name="4952" class="Symbol"
- >{</a
- ><a name="4953" href="Stlc.html#4953" class="Bound"
- >M</a
><a name="4954"
> </a
- ><a name="4955" href="Stlc.html#4955" class="Bound"
- >N</a
- ><a name="4956" class="Symbol"
- >}</a
+ ><a name="4955" class="Symbol"
+ >{</a
+ ><a name="4956" href="Stlc.html#4956" class="Bound"
+ >M</a
><a name="4957"
> </a
- ><a name="4958" class="Symbol"
+ ><a name="4958" href="Stlc.html#4958" class="Bound"
+ >N</a
+ ><a name="4959" class="Symbol"
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+ ><a name="4960"
+ > </a
+ ><a name="4961" class="Symbol"
>→</a
- ><a name="4959"
+ ><a name="4962"
>
</a
- ><a name="4964" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="4967" href="Stlc.html#3612" class="InductiveConstructor Operator"
>if</a
- ><a name="4966"
+ ><a name="4969"
> </a
- ><a name="4967" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="4970" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="4971"
+ ><a name="4974"
> </a
- ><a name="4972" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="4975" href="Stlc.html#3612" class="InductiveConstructor Operator"
>then</a
- ><a name="4976"
+ ><a name="4979"
> </a
- ><a name="4977" href="Stlc.html#4953" class="Bound"
+ ><a name="4980" href="Stlc.html#4956" class="Bound"
>M</a
- ><a name="4978"
+ ><a name="4981"
> </a
- ><a name="4979" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="4982" href="Stlc.html#3612" class="InductiveConstructor Operator"
>else</a
- ><a name="4983"
+ ><a name="4986"
> </a
- ><a name="4984" href="Stlc.html#4955" class="Bound"
+ ><a name="4987" href="Stlc.html#4958" class="Bound"
>N</a
- ><a name="4985"
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> </a
- ><a name="4986" href="Stlc.html#4717" class="Datatype Operator"
+ ><a name="4989" href="Stlc.html#4720" class="Datatype Operator"
>⟹</a
- ><a name="4987"
+ ><a name="4990"
> </a
- ><a name="4988" href="Stlc.html#4953" class="Bound"
+ ><a name="4991" href="Stlc.html#4956" class="Bound"
>M</a
- ><a name="4989"
+ ><a name="4992"
>
</a
- ><a name="4992" href="Stlc.html#4992" class="InductiveConstructor"
+ ><a name="4995" href="Stlc.html#4995" class="InductiveConstructor"
>βif-false</a
- ><a name="5001"
+ ><a name="5004"
> </a
- ><a name="5002" class="Symbol"
+ ><a name="5005" class="Symbol"
>:</a
- ><a name="5003"
+ ><a name="5006"
> </a
- ><a name="5004" class="Symbol"
+ ><a name="5007" class="Symbol"
>∀</a
- ><a name="5005"
- > </a
- ><a name="5006" class="Symbol"
- >{</a
- ><a name="5007" href="Stlc.html#5007" class="Bound"
- >M</a
><a name="5008"
> </a
- ><a name="5009" href="Stlc.html#5009" class="Bound"
- >N</a
- ><a name="5010" class="Symbol"
- >}</a
+ ><a name="5009" class="Symbol"
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+ ><a name="5010" href="Stlc.html#5010" class="Bound"
+ >M</a
><a name="5011"
> </a
- ><a name="5012" class="Symbol"
+ ><a name="5012" href="Stlc.html#5012" class="Bound"
+ >N</a
+ ><a name="5013" class="Symbol"
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+ ><a name="5014"
+ > </a
+ ><a name="5015" class="Symbol"
>→</a
- ><a name="5013"
+ ><a name="5016"
>
</a
- ><a name="5018" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="5021" href="Stlc.html#3612" class="InductiveConstructor Operator"
>if</a
- ><a name="5020"
+ ><a name="5023"
> </a
- ><a name="5021" href="Stlc.html#3594" class="InductiveConstructor"
+ ><a name="5024" href="Stlc.html#3597" class="InductiveConstructor"
>false</a
- ><a name="5026"
+ ><a name="5029"
> </a
- ><a name="5027" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="5030" href="Stlc.html#3612" class="InductiveConstructor Operator"
>then</a
- ><a name="5031"
+ ><a name="5034"
> </a
- ><a name="5032" href="Stlc.html#5007" class="Bound"
+ ><a name="5035" href="Stlc.html#5010" class="Bound"
>M</a
- ><a name="5033"
+ ><a name="5036"
> </a
- ><a name="5034" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="5037" href="Stlc.html#3612" class="InductiveConstructor Operator"
>else</a
- ><a name="5038"
+ ><a name="5041"
> </a
- ><a name="5039" href="Stlc.html#5009" class="Bound"
+ ><a name="5042" href="Stlc.html#5012" class="Bound"
>N</a
- ><a name="5040"
+ ><a name="5043"
> </a
- ><a name="5041" href="Stlc.html#4717" class="Datatype Operator"
+ ><a name="5044" href="Stlc.html#4720" class="Datatype Operator"
>⟹</a
- ><a name="5042"
+ ><a name="5045"
> </a
- ><a name="5043" href="Stlc.html#5009" class="Bound"
+ ><a name="5046" href="Stlc.html#5012" class="Bound"
>N</a
- ><a name="5044"
+ ><a name="5047"
>
</a
- ><a name="5047" href="Stlc.html#5047" class="InductiveConstructor"
+ ><a name="5050" href="Stlc.html#5050" class="InductiveConstructor"
>ξif</a
- ><a name="5050"
+ ><a name="5053"
> </a
- ><a name="5051" class="Symbol"
+ ><a name="5054" class="Symbol"
>:</a
- ><a name="5052"
+ ><a name="5055"
> </a
- ><a name="5053" class="Symbol"
+ ><a name="5056" class="Symbol"
>∀</a
- ><a name="5054"
- > </a
- ><a name="5055" class="Symbol"
- >{</a
- ><a name="5056" href="Stlc.html#5056" class="Bound"
- >L</a
><a name="5057"
> </a
- ><a name="5058" href="Stlc.html#5058" class="Bound"
- >L′</a
+ ><a name="5058" class="Symbol"
+ >{</a
+ ><a name="5059" href="Stlc.html#5059" class="Bound"
+ >L</a
><a name="5060"
> </a
><a name="5061" href="Stlc.html#5061" class="Bound"
- >M</a
- ><a name="5062"
+ >L′</a
+ ><a name="5063"
> </a
- ><a name="5063" href="Stlc.html#5063" class="Bound"
- >N</a
- ><a name="5064" class="Symbol"
- >}</a
+ ><a name="5064" href="Stlc.html#5064" class="Bound"
+ >M</a
><a name="5065"
> </a
- ><a name="5066" class="Symbol"
+ ><a name="5066" href="Stlc.html#5066" class="Bound"
+ >N</a
+ ><a name="5067" class="Symbol"
+ >}</a
+ ><a name="5068"
+ > </a
+ ><a name="5069" class="Symbol"
>→</a
- ><a name="5067"
+ ><a name="5070"
>
</a
- ><a name="5072" href="Stlc.html#5056" class="Bound"
+ ><a name="5075" href="Stlc.html#5059" class="Bound"
>L</a
- ><a name="5073"
+ ><a name="5076"
> </a
- ><a name="5074" href="Stlc.html#4717" class="Datatype Operator"
+ ><a name="5077" href="Stlc.html#4720" class="Datatype Operator"
>⟹</a
- ><a name="5075"
- > </a
- ><a name="5076" href="Stlc.html#5058" class="Bound"
- >L′</a
><a name="5078"
> </a
- ><a name="5079" class="Symbol"
+ ><a name="5079" href="Stlc.html#5061" class="Bound"
+ >L′</a
+ ><a name="5081"
+ > </a
+ ><a name="5082" class="Symbol"
>→</a
- ><a name="5080"
+ ><a name="5083"
>
</a
- ><a name="5089" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="5092" href="Stlc.html#3612" class="InductiveConstructor Operator"
>if</a
- ><a name="5091"
+ ><a name="5094"
> </a
- ><a name="5092" href="Stlc.html#5056" class="Bound"
+ ><a name="5095" href="Stlc.html#5059" class="Bound"
>L</a
- ><a name="5093"
+ ><a name="5096"
> </a
- ><a name="5094" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="5097" href="Stlc.html#3612" class="InductiveConstructor Operator"
>then</a
- ><a name="5098"
+ ><a name="5101"
> </a
- ><a name="5099" href="Stlc.html#5061" class="Bound"
+ ><a name="5102" href="Stlc.html#5064" class="Bound"
>M</a
- ><a name="5100"
+ ><a name="5103"
> </a
- ><a name="5101" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="5104" href="Stlc.html#3612" class="InductiveConstructor Operator"
>else</a
- ><a name="5105"
+ ><a name="5108"
> </a
- ><a name="5106" href="Stlc.html#5063" class="Bound"
+ ><a name="5109" href="Stlc.html#5066" class="Bound"
>N</a
- ><a name="5107"
+ ><a name="5110"
> </a
- ><a name="5108" href="Stlc.html#4717" class="Datatype Operator"
+ ><a name="5111" href="Stlc.html#4720" class="Datatype Operator"
>⟹</a
- ><a name="5109"
- > </a
- ><a name="5110" href="Stlc.html#3609" class="InductiveConstructor Operator"
- >if</a
><a name="5112"
> </a
- ><a name="5113" href="Stlc.html#5058" class="Bound"
- >L′</a
+ ><a name="5113" href="Stlc.html#3612" class="InductiveConstructor Operator"
+ >if</a
><a name="5115"
> </a
- ><a name="5116" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="5116" href="Stlc.html#5061" class="Bound"
+ >L′</a
+ ><a name="5118"
+ > </a
+ ><a name="5119" href="Stlc.html#3612" class="InductiveConstructor Operator"
>then</a
- ><a name="5120"
+ ><a name="5123"
> </a
- ><a name="5121" href="Stlc.html#5061" class="Bound"
+ ><a name="5124" href="Stlc.html#5064" class="Bound"
>M</a
- ><a name="5122"
+ ><a name="5125"
> </a
- ><a name="5123" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="5126" href="Stlc.html#3612" class="InductiveConstructor Operator"
>else</a
- ><a name="5127"
+ ><a name="5130"
> </a
- ><a name="5128" href="Stlc.html#5063" class="Bound"
+ ><a name="5131" href="Stlc.html#5066" class="Bound"
>N</a
>
@@ -2195,665 +2195,665 @@ Example terms.
<pre class="Agda">
-<a name="5193" class="Keyword"
+<a name="5196" class="Keyword"
>infix</a
- ><a name="5198"
- > </a
- ><a name="5199" class="Number"
- >10</a
><a name="5201"
> </a
- ><a name="5202" href="Stlc.html#5242" class="Datatype Operator"
+ ><a name="5202" class="Number"
+ >10</a
+ ><a name="5204"
+ > </a
+ ><a name="5205" href="Stlc.html#5245" class="Datatype Operator"
>_⟹*_</a
- ><a name="5206"
+ ><a name="5209"
>
</a
- ><a name="5208" class="Keyword"
+ ><a name="5211" class="Keyword"
>infixr</a
- ><a name="5214"
+ ><a name="5217"
> </a
- ><a name="5215" class="Number"
+ ><a name="5218" class="Number"
>2</a
- ><a name="5216"
+ ><a name="5219"
> </a
- ><a name="5217" href="Stlc.html#5295" class="InductiveConstructor Operator"
+ ><a name="5220" href="Stlc.html#5298" class="InductiveConstructor Operator"
>_⟹⟨_⟩_</a
- ><a name="5223"
+ ><a name="5226"
>
</a
- ><a name="5224" class="Keyword"
+ ><a name="5227" class="Keyword"
>infix</a
- ><a name="5229"
- > </a
- ><a name="5231" class="Number"
- >3</a
><a name="5232"
- > </a
- ><a name="5233" href="Stlc.html#5275" class="InductiveConstructor Operator"
- >_∎</a
+ > </a
+ ><a name="5234" class="Number"
+ >3</a
><a name="5235"
+ > </a
+ ><a name="5236" href="Stlc.html#5278" class="InductiveConstructor Operator"
+ >_∎</a
+ ><a name="5238"
>
</a
- ><a name="5237" class="Keyword"
+ ><a name="5240" class="Keyword"
>data</a
- ><a name="5241"
+ ><a name="5244"
> </a
- ><a name="5242" href="Stlc.html#5242" class="Datatype Operator"
+ ><a name="5245" href="Stlc.html#5245" class="Datatype Operator"
>_⟹*_</a
- ><a name="5246"
+ ><a name="5249"
> </a
- ><a name="5247" class="Symbol"
+ ><a name="5250" class="Symbol"
>:</a
- ><a name="5248"
+ ><a name="5251"
> </a
- ><a name="5249" href="Stlc.html#3482" class="Datatype"
+ ><a name="5252" href="Stlc.html#3485" class="Datatype"
>Term</a
- ><a name="5253"
+ ><a name="5256"
> </a
- ><a name="5254" class="Symbol"
+ ><a name="5257" class="Symbol"
>→</a
- ><a name="5255"
+ ><a name="5258"
> </a
- ><a name="5256" href="Stlc.html#3482" class="Datatype"
+ ><a name="5259" href="Stlc.html#3485" class="Datatype"
>Term</a
- ><a name="5260"
+ ><a name="5263"
> </a
- ><a name="5261" class="Symbol"
+ ><a name="5264" class="Symbol"
>→</a
- ><a name="5262"
+ ><a name="5265"
> </a
- ><a name="5263" class="PrimitiveType"
+ ><a name="5266" class="PrimitiveType"
>Set</a
- ><a name="5266"
+ ><a name="5269"
> </a
- ><a name="5267" class="Keyword"
+ ><a name="5270" class="Keyword"
>where</a
- ><a name="5272"
+ ><a name="5275"
>
</a
- ><a name="5275" href="Stlc.html#5275" class="InductiveConstructor Operator"
+ ><a name="5278" href="Stlc.html#5278" class="InductiveConstructor Operator"
>_∎</a
- ><a name="5277"
+ ><a name="5280"
> </a
- ><a name="5278" class="Symbol"
+ ><a name="5281" class="Symbol"
>:</a
- ><a name="5279"
+ ><a name="5282"
> </a
- ><a name="5280" class="Symbol"
+ ><a name="5283" class="Symbol"
>∀</a
- ><a name="5281"
+ ><a name="5284"
> </a
- ><a name="5282" href="Stlc.html#5282" class="Bound"
+ ><a name="5285" href="Stlc.html#5285" class="Bound"
>M</a
- ><a name="5283"
+ ><a name="5286"
> </a
- ><a name="5284" class="Symbol"
+ ><a name="5287" class="Symbol"
>→</a
- ><a name="5285"
+ ><a name="5288"
> </a
- ><a name="5286" href="Stlc.html#5282" class="Bound"
+ ><a name="5289" href="Stlc.html#5285" class="Bound"
>M</a
- ><a name="5287"
- > </a
- ><a name="5288" href="Stlc.html#5242" class="Datatype Operator"
- >⟹*</a
><a name="5290"
> </a
- ><a name="5291" href="Stlc.html#5282" class="Bound"
+ ><a name="5291" href="Stlc.html#5245" class="Datatype Operator"
+ >⟹*</a
+ ><a name="5293"
+ > </a
+ ><a name="5294" href="Stlc.html#5285" class="Bound"
>M</a
- ><a name="5292"
+ ><a name="5295"
>
</a
- ><a name="5295" href="Stlc.html#5295" class="InductiveConstructor Operator"
+ ><a name="5298" href="Stlc.html#5298" class="InductiveConstructor Operator"
>_⟹⟨_⟩_</a
- ><a name="5301"
+ ><a name="5304"
> </a
- ><a name="5302" class="Symbol"
+ ><a name="5305" class="Symbol"
>:</a
- ><a name="5303"
+ ><a name="5306"
> </a
- ><a name="5304" class="Symbol"
+ ><a name="5307" class="Symbol"
>∀</a
- ><a name="5305"
+ ><a name="5308"
> </a
- ><a name="5306" href="Stlc.html#5306" class="Bound"
- >L</a
- ><a name="5307"
- > </a
- ><a name="5308" class="Symbol"
- >{</a
><a name="5309" href="Stlc.html#5309" class="Bound"
- >M</a
+ >L</a
><a name="5310"
> </a
- ><a name="5311" href="Stlc.html#5311" class="Bound"
- >N</a
- ><a name="5312" class="Symbol"
- >}</a
+ ><a name="5311" class="Symbol"
+ >{</a
+ ><a name="5312" href="Stlc.html#5312" class="Bound"
+ >M</a
><a name="5313"
> </a
- ><a name="5314" class="Symbol"
- >→</a
- ><a name="5315"
+ ><a name="5314" href="Stlc.html#5314" class="Bound"
+ >N</a
+ ><a name="5315" class="Symbol"
+ >}</a
+ ><a name="5316"
> </a
- ><a name="5316" href="Stlc.html#5306" class="Bound"
+ ><a name="5317" class="Symbol"
+ >→</a
+ ><a name="5318"
+ > </a
+ ><a name="5319" href="Stlc.html#5309" class="Bound"
>L</a
- ><a name="5317"
+ ><a name="5320"
> </a
- ><a name="5318" href="Stlc.html#4717" class="Datatype Operator"
+ ><a name="5321" href="Stlc.html#4720" class="Datatype Operator"
>⟹</a
- ><a name="5319"
+ ><a name="5322"
> </a
- ><a name="5320" href="Stlc.html#5309" class="Bound"
+ ><a name="5323" href="Stlc.html#5312" class="Bound"
>M</a
- ><a name="5321"
+ ><a name="5324"
> </a
- ><a name="5322" class="Symbol"
+ ><a name="5325" class="Symbol"
>→</a
- ><a name="5323"
+ ><a name="5326"
> </a
- ><a name="5324" href="Stlc.html#5309" class="Bound"
+ ><a name="5327" href="Stlc.html#5312" class="Bound"
>M</a
- ><a name="5325"
- > </a
- ><a name="5326" href="Stlc.html#5242" class="Datatype Operator"
- >⟹*</a
><a name="5328"
> </a
- ><a name="5329" href="Stlc.html#5311" class="Bound"
- >N</a
- ><a name="5330"
- > </a
- ><a name="5331" class="Symbol"
- >→</a
- ><a name="5332"
- > </a
- ><a name="5333" href="Stlc.html#5306" class="Bound"
- >L</a
- ><a name="5334"
- > </a
- ><a name="5335" href="Stlc.html#5242" class="Datatype Operator"
+ ><a name="5329" href="Stlc.html#5245" class="Datatype Operator"
>⟹*</a
+ ><a name="5331"
+ > </a
+ ><a name="5332" href="Stlc.html#5314" class="Bound"
+ >N</a
+ ><a name="5333"
+ > </a
+ ><a name="5334" class="Symbol"
+ >→</a
+ ><a name="5335"
+ > </a
+ ><a name="5336" href="Stlc.html#5309" class="Bound"
+ >L</a
><a name="5337"
> </a
- ><a name="5338" href="Stlc.html#5311" class="Bound"
+ ><a name="5338" href="Stlc.html#5245" class="Datatype Operator"
+ >⟹*</a
+ ><a name="5340"
+ > </a
+ ><a name="5341" href="Stlc.html#5314" class="Bound"
>N</a
- ><a name="5339"
+ ><a name="5342"
>
</a
- ><a name="5343" href="Stlc.html#5343" class="Function"
+ ><a name="5346" href="Stlc.html#5346" class="Function"
>reduction₁</a
- ><a name="5353"
+ ><a name="5356"
> </a
- ><a name="5354" class="Symbol"
+ ><a name="5357" class="Symbol"
>:</a
- ><a name="5355"
+ ><a name="5358"
> </a
- ><a name="5356" href="Stlc.html#3904" class="Function"
+ ><a name="5359" href="Stlc.html#3907" class="Function"
>not</a
- ><a name="5359"
+ ><a name="5362"
> </a
- ><a name="5360" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="5363" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
- ><a name="5361"
+ ><a name="5364"
> </a
- ><a name="5362" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="5365" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="5366"
- > </a
- ><a name="5367" href="Stlc.html#5242" class="Datatype Operator"
- >⟹*</a
><a name="5369"
> </a
- ><a name="5370" href="Stlc.html#3594" class="InductiveConstructor"
+ ><a name="5370" href="Stlc.html#5245" class="Datatype Operator"
+ >⟹*</a
+ ><a name="5372"
+ > </a
+ ><a name="5373" href="Stlc.html#3597" class="InductiveConstructor"
>false</a
- ><a name="5375"
+ ><a name="5378"
>
</a
- ><a name="5376" href="Stlc.html#5343" class="Function"
+ ><a name="5379" href="Stlc.html#5346" class="Function"
>reduction₁</a
- ><a name="5386"
+ ><a name="5389"
> </a
- ><a name="5387" class="Symbol"
+ ><a name="5390" class="Symbol"
>=</a
- ><a name="5388"
+ ><a name="5391"
>
</a
- ><a name="5393" href="Stlc.html#3904" class="Function"
+ ><a name="5396" href="Stlc.html#3907" class="Function"
>not</a
- ><a name="5396"
+ ><a name="5399"
> </a
- ><a name="5397" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="5400" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
- ><a name="5398"
+ ><a name="5401"
> </a
- ><a name="5399" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="5402" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="5403"
+ ><a name="5406"
>
</a
- ><a name="5406" href="Stlc.html#5295" class="InductiveConstructor Operator"
+ ><a name="5409" href="Stlc.html#5298" class="InductiveConstructor Operator"
>⟹⟨</a
- ><a name="5408"
+ ><a name="5411"
> </a
- ><a name="5409" href="Stlc.html#4749" class="InductiveConstructor"
+ ><a name="5412" href="Stlc.html#4752" class="InductiveConstructor"
>βλ·</a
- ><a name="5412"
+ ><a name="5415"
> </a
- ><a name="5413" href="Stlc.html#4136" class="InductiveConstructor"
+ ><a name="5416" href="Stlc.html#4139" class="InductiveConstructor"
>value-true</a
- ><a name="5423"
+ ><a name="5426"
> </a
- ><a name="5424" href="Stlc.html#5295" class="InductiveConstructor Operator"
+ ><a name="5427" href="Stlc.html#5298" class="InductiveConstructor Operator"
>⟩</a
- ><a name="5425"
+ ><a name="5428"
>
</a
- ><a name="5430" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="5433" href="Stlc.html#3612" class="InductiveConstructor Operator"
>if</a
- ><a name="5432"
+ ><a name="5435"
> </a
- ><a name="5433" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="5436" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="5437"
+ ><a name="5440"
> </a
- ><a name="5438" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="5441" href="Stlc.html#3612" class="InductiveConstructor Operator"
>then</a
- ><a name="5442"
+ ><a name="5445"
> </a
- ><a name="5443" href="Stlc.html#3594" class="InductiveConstructor"
+ ><a name="5446" href="Stlc.html#3597" class="InductiveConstructor"
>false</a
- ><a name="5448"
+ ><a name="5451"
> </a
- ><a name="5449" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="5452" href="Stlc.html#3612" class="InductiveConstructor Operator"
>else</a
- ><a name="5453"
+ ><a name="5456"
> </a
- ><a name="5454" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="5457" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="5458"
+ ><a name="5461"
>
</a
- ><a name="5461" href="Stlc.html#5295" class="InductiveConstructor Operator"
+ ><a name="5464" href="Stlc.html#5298" class="InductiveConstructor Operator"
>⟹⟨</a
- ><a name="5463"
+ ><a name="5466"
> </a
- ><a name="5464" href="Stlc.html#4939" class="InductiveConstructor"
+ ><a name="5467" href="Stlc.html#4942" class="InductiveConstructor"
>βif-true</a
- ><a name="5472"
+ ><a name="5475"
> </a
- ><a name="5473" href="Stlc.html#5295" class="InductiveConstructor Operator"
+ ><a name="5476" href="Stlc.html#5298" class="InductiveConstructor Operator"
>⟩</a
- ><a name="5474"
+ ><a name="5477"
>
</a
- ><a name="5479" href="Stlc.html#3594" class="InductiveConstructor"
+ ><a name="5482" href="Stlc.html#3597" class="InductiveConstructor"
>false</a
- ><a name="5484"
+ ><a name="5487"
>
</a
- ><a name="5487" href="Stlc.html#5275" class="InductiveConstructor Operator"
+ ><a name="5490" href="Stlc.html#5278" class="InductiveConstructor Operator"
>∎</a
- ><a name="5488"
+ ><a name="5491"
>
</a
- ><a name="5490" href="Stlc.html#5490" class="Function"
+ ><a name="5493" href="Stlc.html#5493" class="Function"
>reduction₂</a
- ><a name="5500"
+ ><a name="5503"
> </a
- ><a name="5501" class="Symbol"
+ ><a name="5504" class="Symbol"
>:</a
- ><a name="5502"
+ ><a name="5505"
> </a
- ><a name="5503" href="Stlc.html#3908" class="Function"
+ ><a name="5506" href="Stlc.html#3911" class="Function"
>two</a
- ><a name="5506"
+ ><a name="5509"
> </a
- ><a name="5507" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="5510" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
- ><a name="5508"
+ ><a name="5511"
> </a
- ><a name="5509" href="Stlc.html#3904" class="Function"
+ ><a name="5512" href="Stlc.html#3907" class="Function"
>not</a
- ><a name="5512"
+ ><a name="5515"
> </a
- ><a name="5513" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="5516" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
- ><a name="5514"
+ ><a name="5517"
> </a
- ><a name="5515" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="5518" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="5519"
- > </a
- ><a name="5520" href="Stlc.html#5242" class="Datatype Operator"
- >⟹*</a
><a name="5522"
> </a
- ><a name="5523" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="5523" href="Stlc.html#5245" class="Datatype Operator"
+ >⟹*</a
+ ><a name="5525"
+ > </a
+ ><a name="5526" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="5527"
+ ><a name="5530"
>
</a
- ><a name="5528" href="Stlc.html#5490" class="Function"
+ ><a name="5531" href="Stlc.html#5493" class="Function"
>reduction₂</a
- ><a name="5538"
+ ><a name="5541"
> </a
- ><a name="5539" class="Symbol"
+ ><a name="5542" class="Symbol"
>=</a
- ><a name="5540"
+ ><a name="5543"
>
</a
- ><a name="5545" href="Stlc.html#3908" class="Function"
+ ><a name="5548" href="Stlc.html#3911" class="Function"
>two</a
- ><a name="5548"
+ ><a name="5551"
> </a
- ><a name="5549" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="5552" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
- ><a name="5550"
+ ><a name="5553"
> </a
- ><a name="5551" href="Stlc.html#3904" class="Function"
+ ><a name="5554" href="Stlc.html#3907" class="Function"
>not</a
- ><a name="5554"
+ ><a name="5557"
> </a
- ><a name="5555" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="5558" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
- ><a name="5556"
+ ><a name="5559"
> </a
- ><a name="5557" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="5560" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="5561"
+ ><a name="5564"
>
</a
- ><a name="5564" href="Stlc.html#5295" class="InductiveConstructor Operator"
+ ><a name="5567" href="Stlc.html#5298" class="InductiveConstructor Operator"
>⟹⟨</a
- ><a name="5566"
+ ><a name="5569"
> </a
- ><a name="5567" href="Stlc.html#4819" class="InductiveConstructor"
+ ><a name="5570" href="Stlc.html#4822" class="InductiveConstructor"
>ξ·₁</a
- ><a name="5570"
+ ><a name="5573"
> </a
- ><a name="5571" class="Symbol"
+ ><a name="5574" class="Symbol"
>(</a
- ><a name="5572" href="Stlc.html#4749" class="InductiveConstructor"
+ ><a name="5575" href="Stlc.html#4752" class="InductiveConstructor"
>βλ·</a
- ><a name="5575"
+ ><a name="5578"
> </a
- ><a name="5576" href="Stlc.html#4087" class="InductiveConstructor"
+ ><a name="5579" href="Stlc.html#4090" class="InductiveConstructor"
>value-λ</a
- ><a name="5583" class="Symbol"
+ ><a name="5586" class="Symbol"
>)</a
- ><a name="5584"
+ ><a name="5587"
> </a
- ><a name="5585" href="Stlc.html#5295" class="InductiveConstructor Operator"
+ ><a name="5588" href="Stlc.html#5298" class="InductiveConstructor Operator"
>⟩</a
- ><a name="5586"
+ ><a name="5589"
>
</a
- ><a name="5591" class="Symbol"
+ ><a name="5594" class="Symbol"
>(</a
- ><a name="5592" href="Stlc.html#3517" class="InductiveConstructor Operator"
+ ><a name="5595" href="Stlc.html#3520" class="InductiveConstructor Operator"
>λ[</a
- ><a name="5594"
+ ><a name="5597"
> </a
- ><a name="5595" href="Stlc.html#3874" class="Function"
+ ><a name="5598" href="Stlc.html#3877" class="Function"
>x</a
- ><a name="5596"
+ ><a name="5599"
> </a
- ><a name="5597" href="Stlc.html#3517" class="InductiveConstructor Operator"
+ ><a name="5600" href="Stlc.html#3520" class="InductiveConstructor Operator"
>∶</a
- ><a name="5598"
+ ><a name="5601"
> </a
- ><a name="5599" href="Stlc.html#2577" class="InductiveConstructor"
+ ><a name="5602" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
- ><a name="5600"
+ ><a name="5603"
> </a
- ><a name="5601" href="Stlc.html#3517" class="InductiveConstructor Operator"
+ ><a name="5604" href="Stlc.html#3520" class="InductiveConstructor Operator"
>]</a
- ><a name="5602"
+ ><a name="5605"
> </a
- ><a name="5603" href="Stlc.html#3904" class="Function"
+ ><a name="5606" href="Stlc.html#3907" class="Function"
>not</a
- ><a name="5606"
+ ><a name="5609"
> </a
- ><a name="5607" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="5610" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
- ><a name="5608"
+ ><a name="5611"
> </a
- ><a name="5609" class="Symbol"
+ ><a name="5612" class="Symbol"
>(</a
- ><a name="5610" href="Stlc.html#3904" class="Function"
+ ><a name="5613" href="Stlc.html#3907" class="Function"
>not</a
- ><a name="5613"
+ ><a name="5616"
> </a
- ><a name="5614" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="5617" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
- ><a name="5615"
+ ><a name="5618"
> </a
- ><a name="5616" href="Stlc.html#3501" class="InductiveConstructor"
+ ><a name="5619" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
- ><a name="5617"
+ ><a name="5620"
> </a
- ><a name="5618" href="Stlc.html#3874" class="Function"
+ ><a name="5621" href="Stlc.html#3877" class="Function"
>x</a
- ><a name="5619" class="Symbol"
+ ><a name="5622" class="Symbol"
>))</a
- ><a name="5621"
+ ><a name="5624"
> </a
- ><a name="5622" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="5625" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
- ><a name="5623"
+ ><a name="5626"
> </a
- ><a name="5624" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="5627" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="5628"
+ ><a name="5631"
>
</a
- ><a name="5631" href="Stlc.html#5295" class="InductiveConstructor Operator"
+ ><a name="5634" href="Stlc.html#5298" class="InductiveConstructor Operator"
>⟹⟨</a
- ><a name="5633"
+ ><a name="5636"
> </a
- ><a name="5634" href="Stlc.html#4749" class="InductiveConstructor"
+ ><a name="5637" href="Stlc.html#4752" class="InductiveConstructor"
>βλ·</a
- ><a name="5637"
+ ><a name="5640"
> </a
- ><a name="5638" href="Stlc.html#4136" class="InductiveConstructor"
+ ><a name="5641" href="Stlc.html#4139" class="InductiveConstructor"
>value-true</a
- ><a name="5648"
+ ><a name="5651"
> </a
- ><a name="5649" href="Stlc.html#5295" class="InductiveConstructor Operator"
+ ><a name="5652" href="Stlc.html#5298" class="InductiveConstructor Operator"
>⟩</a
- ><a name="5650"
+ ><a name="5653"
>
</a
- ><a name="5655" href="Stlc.html#3904" class="Function"
+ ><a name="5658" href="Stlc.html#3907" class="Function"
>not</a
- ><a name="5658"
+ ><a name="5661"
> </a
- ><a name="5659" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="5662" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
- ><a name="5660"
+ ><a name="5663"
> </a
- ><a name="5661" class="Symbol"
+ ><a name="5664" class="Symbol"
>(</a
- ><a name="5662" href="Stlc.html#3904" class="Function"
+ ><a name="5665" href="Stlc.html#3907" class="Function"
>not</a
- ><a name="5665"
+ ><a name="5668"
> </a
- ><a name="5666" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="5669" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
- ><a name="5667"
+ ><a name="5670"
> </a
- ><a name="5668" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="5671" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="5672" class="Symbol"
+ ><a name="5675" class="Symbol"
>)</a
- ><a name="5673"
+ ><a name="5676"
>
</a
- ><a name="5676" href="Stlc.html#5295" class="InductiveConstructor Operator"
+ ><a name="5679" href="Stlc.html#5298" class="InductiveConstructor Operator"
>⟹⟨</a
- ><a name="5678"
+ ><a name="5681"
> </a
- ><a name="5679" href="Stlc.html#4872" class="InductiveConstructor"
+ ><a name="5682" href="Stlc.html#4875" class="InductiveConstructor"
>ξ·₂</a
- ><a name="5682"
+ ><a name="5685"
> </a
- ><a name="5683" href="Stlc.html#4087" class="InductiveConstructor"
+ ><a name="5686" href="Stlc.html#4090" class="InductiveConstructor"
>value-λ</a
- ><a name="5690"
+ ><a name="5693"
> </a
- ><a name="5691" class="Symbol"
+ ><a name="5694" class="Symbol"
>(</a
- ><a name="5692" href="Stlc.html#4749" class="InductiveConstructor"
+ ><a name="5695" href="Stlc.html#4752" class="InductiveConstructor"
>βλ·</a
- ><a name="5695"
+ ><a name="5698"
> </a
- ><a name="5696" href="Stlc.html#4136" class="InductiveConstructor"
+ ><a name="5699" href="Stlc.html#4139" class="InductiveConstructor"
>value-true</a
- ><a name="5706" class="Symbol"
+ ><a name="5709" class="Symbol"
>)</a
- ><a name="5707"
+ ><a name="5710"
> </a
- ><a name="5708" href="Stlc.html#5295" class="InductiveConstructor Operator"
+ ><a name="5711" href="Stlc.html#5298" class="InductiveConstructor Operator"
>⟩</a
- ><a name="5709"
+ ><a name="5712"
>
</a
- ><a name="5714" href="Stlc.html#3904" class="Function"
+ ><a name="5717" href="Stlc.html#3907" class="Function"
>not</a
- ><a name="5717"
+ ><a name="5720"
> </a
- ><a name="5718" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="5721" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
- ><a name="5719"
+ ><a name="5722"
> </a
- ><a name="5720" class="Symbol"
+ ><a name="5723" class="Symbol"
>(</a
- ><a name="5721" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="5724" href="Stlc.html#3612" class="InductiveConstructor Operator"
>if</a
- ><a name="5723"
+ ><a name="5726"
> </a
- ><a name="5724" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="5727" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="5728"
+ ><a name="5731"
> </a
- ><a name="5729" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="5732" href="Stlc.html#3612" class="InductiveConstructor Operator"
>then</a
- ><a name="5733"
+ ><a name="5736"
> </a
- ><a name="5734" href="Stlc.html#3594" class="InductiveConstructor"
+ ><a name="5737" href="Stlc.html#3597" class="InductiveConstructor"
>false</a
- ><a name="5739"
+ ><a name="5742"
> </a
- ><a name="5740" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="5743" href="Stlc.html#3612" class="InductiveConstructor Operator"
>else</a
- ><a name="5744"
+ ><a name="5747"
> </a
- ><a name="5745" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="5748" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="5749" class="Symbol"
+ ><a name="5752" class="Symbol"
>)</a
- ><a name="5750"
+ ><a name="5753"
>
</a
- ><a name="5753" href="Stlc.html#5295" class="InductiveConstructor Operator"
+ ><a name="5756" href="Stlc.html#5298" class="InductiveConstructor Operator"
>⟹⟨</a
- ><a name="5755"
+ ><a name="5758"
> </a
- ><a name="5756" href="Stlc.html#4872" class="InductiveConstructor"
+ ><a name="5759" href="Stlc.html#4875" class="InductiveConstructor"
>ξ·₂</a
- ><a name="5759"
+ ><a name="5762"
> </a
- ><a name="5760" href="Stlc.html#4087" class="InductiveConstructor"
+ ><a name="5763" href="Stlc.html#4090" class="InductiveConstructor"
>value-λ</a
- ><a name="5767"
+ ><a name="5770"
> </a
- ><a name="5768" href="Stlc.html#4939" class="InductiveConstructor"
+ ><a name="5771" href="Stlc.html#4942" class="InductiveConstructor"
>βif-true</a
- ><a name="5776"
- > </a
- ><a name="5778" href="Stlc.html#5295" class="InductiveConstructor Operator"
- >⟩</a
><a name="5779"
+ > </a
+ ><a name="5781" href="Stlc.html#5298" class="InductiveConstructor Operator"
+ >⟩</a
+ ><a name="5782"
>
</a
- ><a name="5784" href="Stlc.html#3904" class="Function"
+ ><a name="5787" href="Stlc.html#3907" class="Function"
>not</a
- ><a name="5787"
+ ><a name="5790"
> </a
- ><a name="5788" href="Stlc.html#3553" class="InductiveConstructor Operator"
+ ><a name="5791" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
- ><a name="5789"
+ ><a name="5792"
> </a
- ><a name="5790" href="Stlc.html#3594" class="InductiveConstructor"
+ ><a name="5793" href="Stlc.html#3597" class="InductiveConstructor"
>false</a
- ><a name="5795"
+ ><a name="5798"
>
</a
- ><a name="5798" href="Stlc.html#5295" class="InductiveConstructor Operator"
+ ><a name="5801" href="Stlc.html#5298" class="InductiveConstructor Operator"
>⟹⟨</a
- ><a name="5800"
+ ><a name="5803"
> </a
- ><a name="5801" href="Stlc.html#4749" class="InductiveConstructor"
+ ><a name="5804" href="Stlc.html#4752" class="InductiveConstructor"
>βλ·</a
- ><a name="5804"
+ ><a name="5807"
> </a
- ><a name="5805" href="Stlc.html#4163" class="InductiveConstructor"
+ ><a name="5808" href="Stlc.html#4166" class="InductiveConstructor"
>value-false</a
- ><a name="5816"
+ ><a name="5819"
> </a
- ><a name="5817" href="Stlc.html#5295" class="InductiveConstructor Operator"
+ ><a name="5820" href="Stlc.html#5298" class="InductiveConstructor Operator"
>⟩</a
- ><a name="5818"
+ ><a name="5821"
>
</a
- ><a name="5823" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="5826" href="Stlc.html#3612" class="InductiveConstructor Operator"
>if</a
- ><a name="5825"
+ ><a name="5828"
> </a
- ><a name="5826" href="Stlc.html#3594" class="InductiveConstructor"
+ ><a name="5829" href="Stlc.html#3597" class="InductiveConstructor"
>false</a
- ><a name="5831"
+ ><a name="5834"
> </a
- ><a name="5832" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="5835" href="Stlc.html#3612" class="InductiveConstructor Operator"
>then</a
- ><a name="5836"
+ ><a name="5839"
> </a
- ><a name="5837" href="Stlc.html#3594" class="InductiveConstructor"
+ ><a name="5840" href="Stlc.html#3597" class="InductiveConstructor"
>false</a
- ><a name="5842"
+ ><a name="5845"
> </a
- ><a name="5843" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="5846" href="Stlc.html#3612" class="InductiveConstructor Operator"
>else</a
- ><a name="5847"
+ ><a name="5850"
> </a
- ><a name="5848" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="5851" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="5852"
+ ><a name="5855"
>
</a
- ><a name="5855" href="Stlc.html#5295" class="InductiveConstructor Operator"
+ ><a name="5858" href="Stlc.html#5298" class="InductiveConstructor Operator"
>⟹⟨</a
- ><a name="5857"
+ ><a name="5860"
> </a
- ><a name="5858" href="Stlc.html#4992" class="InductiveConstructor"
+ ><a name="5861" href="Stlc.html#4995" class="InductiveConstructor"
>βif-false</a
- ><a name="5867"
+ ><a name="5870"
> </a
- ><a name="5868" href="Stlc.html#5295" class="InductiveConstructor Operator"
+ ><a name="5871" href="Stlc.html#5298" class="InductiveConstructor Operator"
>⟩</a
- ><a name="5869"
+ ><a name="5872"
>
</a
- ><a name="5874" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="5877" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="5878"
+ ><a name="5881"
>
</a
- ><a name="5881" href="Stlc.html#5275" class="InductiveConstructor Operator"
+ ><a name="5884" href="Stlc.html#5278" class="InductiveConstructor Operator"
>∎</a
>
@@ -2867,683 +2867,683 @@ Much of the above, though not all, can be filled in using C-c C-r and C-c C-s.
<pre class="Agda">
-<a name="6005" href="Stlc.html#6005" class="Function"
+<a name="6008" href="Stlc.html#6008" class="Function"
>Context</a
- ><a name="6012"
+ ><a name="6015"
> </a
- ><a name="6013" class="Symbol"
+ ><a name="6016" class="Symbol"
>:</a
- ><a name="6014"
+ ><a name="6017"
> </a
- ><a name="6015" class="PrimitiveType"
+ ><a name="6018" class="PrimitiveType"
>Set</a
- ><a name="6018"
+ ><a name="6021"
>
</a
- ><a name="6019" href="Stlc.html#6005" class="Function"
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- ><a name="6026"
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> </a
- ><a name="6027" class="Symbol"
+ ><a name="6030" class="Symbol"
>=</a
- ><a name="6028"
+ ><a name="6031"
> </a
- ><a name="6029" href="Maps.html#10132" class="Function"
+ ><a name="6032" href="Maps.html#10132" class="Function"
>PartialMap</a
- ><a name="6039"
+ ><a name="6042"
> </a
- ><a name="6040" href="Stlc.html#2531" class="Datatype"
+ ><a name="6043" href="Stlc.html#2531" class="Datatype"
>Type</a
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+ ><a name="6047"
>
</a
- ><a name="6046" class="Keyword"
+ ><a name="6049" class="Keyword"
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- ><a name="6051"
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- ><a name="6052" class="Number"
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><a name="6054"
> </a
- ><a name="6055" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6055" class="Number"
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+ ><a name="6057"
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+ ><a name="6058" href="Stlc.html#6070" class="Datatype Operator"
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- ><a name="6060"
+ ><a name="6063"
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</a
- ><a name="6062" class="Keyword"
+ ><a name="6065" class="Keyword"
>data</a
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+ ><a name="6069"
> </a
- ><a name="6067" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6070" href="Stlc.html#6070" class="Datatype Operator"
>_⊢_∶_</a
- ><a name="6072"
+ ><a name="6075"
> </a
- ><a name="6073" class="Symbol"
+ ><a name="6076" class="Symbol"
>:</a
- ><a name="6074"
+ ><a name="6077"
> </a
- ><a name="6075" href="Stlc.html#6005" class="Function"
+ ><a name="6078" href="Stlc.html#6008" class="Function"
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- ><a name="6082"
+ ><a name="6085"
> </a
- ><a name="6083" class="Symbol"
+ ><a name="6086" class="Symbol"
>→</a
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+ ><a name="6087"
> </a
- ><a name="6085" href="Stlc.html#3482" class="Datatype"
+ ><a name="6088" href="Stlc.html#3485" class="Datatype"
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> </a
- ><a name="6090" class="Symbol"
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>→</a
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+ ><a name="6094"
> </a
- ><a name="6092" href="Stlc.html#2531" class="Datatype"
+ ><a name="6095" href="Stlc.html#2531" class="Datatype"
>Type</a
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> </a
- ><a name="6097" class="Symbol"
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>→</a
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+ ><a name="6101"
> </a
- ><a name="6099" class="PrimitiveType"
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> </a
- ><a name="6103" class="Keyword"
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>where</a
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+ ><a name="6111"
>
</a
- ><a name="6111" href="Stlc.html#6111" class="InductiveConstructor"
+ ><a name="6114" href="Stlc.html#6114" class="InductiveConstructor"
>Ax</a
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> </a
- ><a name="6114" class="Symbol"
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>:</a
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> </a
- ><a name="6116" class="Symbol"
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- ><a name="6118" class="Symbol"
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- ><a name="6119" href="Stlc.html#6119" class="Bound"
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><a name="6120"
> </a
- ><a name="6121" href="Stlc.html#6121" class="Bound"
- >x</a
- ><a name="6122"
+ ><a name="6121" class="Symbol"
+ >{</a
+ ><a name="6122" href="Stlc.html#6122" class="Bound"
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+ ><a name="6123"
> </a
- ><a name="6123" href="Stlc.html#6123" class="Bound"
- >A</a
- ><a name="6124" class="Symbol"
- >}</a
+ ><a name="6124" href="Stlc.html#6124" class="Bound"
+ >x</a
><a name="6125"
> </a
- ><a name="6126" class="Symbol"
+ ><a name="6126" href="Stlc.html#6126" class="Bound"
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+ ><a name="6127" class="Symbol"
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+ ><a name="6128"
+ > </a
+ ><a name="6129" class="Symbol"
>→</a
- ><a name="6127"
+ ><a name="6130"
>
</a
- ><a name="6132" href="Stlc.html#6119" class="Bound"
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>Γ</a
- ><a name="6133"
+ ><a name="6136"
> </a
- ><a name="6134" href="Stlc.html#6121" class="Bound"
+ ><a name="6137" href="Stlc.html#6124" class="Bound"
>x</a
- ><a name="6135"
+ ><a name="6138"
> </a
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- ><a name="6137"
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> </a
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- ><a name="6142"
+ ><a name="6145"
> </a
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- ><a name="6144"
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> </a
- ><a name="6145" class="Symbol"
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>→</a
- ><a name="6146"
+ ><a name="6149"
>
</a
- ><a name="6151" href="Stlc.html#6119" class="Bound"
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>Γ</a
- ><a name="6152"
+ ><a name="6155"
> </a
- ><a name="6153" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6156" href="Stlc.html#6070" class="Datatype Operator"
>⊢</a
- ><a name="6154"
+ ><a name="6157"
> </a
- ><a name="6155" href="Stlc.html#3501" class="InductiveConstructor"
+ ><a name="6158" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
- ><a name="6156"
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> </a
- ><a name="6157" href="Stlc.html#6121" class="Bound"
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>x</a
- ><a name="6158"
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> </a
- ><a name="6159" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6162" href="Stlc.html#6070" class="Datatype Operator"
>∶</a
- ><a name="6160"
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> </a
- ><a name="6161" href="Stlc.html#6123" class="Bound"
+ ><a name="6164" href="Stlc.html#6126" class="Bound"
>A</a
- ><a name="6162"
+ ><a name="6165"
>
</a
- ><a name="6165" href="Stlc.html#6165" class="InductiveConstructor"
+ ><a name="6168" href="Stlc.html#6168" class="InductiveConstructor"
>⇒-I</a
- ><a name="6168"
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> </a
- ><a name="6169" class="Symbol"
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>:</a
- ><a name="6170"
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> </a
- ><a name="6171" class="Symbol"
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>∀</a
- ><a name="6172"
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- >{</a
- ><a name="6174" href="Stlc.html#6174" class="Bound"
- >Γ</a
><a name="6175"
> </a
- ><a name="6176" href="Stlc.html#6176" class="Bound"
+ ><a name="6176" class="Symbol"
+ >{</a
+ ><a name="6177" href="Stlc.html#6177" class="Bound"
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>x</a
- ><a name="6177"
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> </a
- ><a name="6178" href="Stlc.html#6178" class="Bound"
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>N</a
- ><a name="6179"
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> </a
- ><a name="6180" href="Stlc.html#6180" class="Bound"
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>A</a
- ><a name="6181"
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- ><a name="6183" class="Symbol"
- >}</a
><a name="6184"
> </a
- ><a name="6185" class="Symbol"
- >→</a
- ><a name="6186"
- >
- </a
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- ><a name="6192"
- > </a
- ><a name="6193" href="Maps.html#10368" class="Function Operator"
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- ><a name="6194"
- > </a
- ><a name="6195" href="Stlc.html#6176" class="Bound"
- >x</a
- ><a name="6196"
- > </a
- ><a name="6197" href="Maps.html#10368" class="Function Operator"
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- ><a name="6198"
- > </a
- ><a name="6199" href="Stlc.html#6180" class="Bound"
- >A</a
- ><a name="6200"
- > </a
- ><a name="6201" href="Stlc.html#6067" class="Datatype Operator"
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- ><a name="6202"
- > </a
- ><a name="6203" href="Stlc.html#6178" class="Bound"
- >N</a
- ><a name="6204"
- > </a
- ><a name="6205" href="Stlc.html#6067" class="Datatype Operator"
- >∶</a
- ><a name="6206"
- > </a
- ><a name="6207" href="Stlc.html#6182" class="Bound"
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>B</a
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> </a
- ><a name="6209" class="Symbol"
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>→</a
- ><a name="6210"
+ ><a name="6189"
>
</a
- ><a name="6215" href="Stlc.html#6174" class="Bound"
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>Γ</a
- ><a name="6216"
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> </a
- ><a name="6217" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6196" href="Maps.html#10368" class="Function Operator"
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+ ><a name="6197"
+ > </a
+ ><a name="6198" href="Stlc.html#6179" class="Bound"
+ >x</a
+ ><a name="6199"
+ > </a
+ ><a name="6200" href="Maps.html#10368" class="Function Operator"
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+ ><a name="6201"
+ > </a
+ ><a name="6202" href="Stlc.html#6183" class="Bound"
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+ ><a name="6203"
+ > </a
+ ><a name="6204" href="Stlc.html#6070" class="Datatype Operator"
>⊢</a
- ><a name="6218"
+ ><a name="6205"
> </a
- ><a name="6219" href="Stlc.html#3517" class="InductiveConstructor Operator"
- >λ[</a
+ ><a name="6206" href="Stlc.html#6181" class="Bound"
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+ ><a name="6207"
+ > </a
+ ><a name="6208" href="Stlc.html#6070" class="Datatype Operator"
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+ ><a name="6209"
+ > </a
+ ><a name="6210" href="Stlc.html#6185" class="Bound"
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+ ><a name="6212" class="Symbol"
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+ ><a name="6213"
+ >
+ </a
+ ><a name="6218" href="Stlc.html#6177" class="Bound"
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+ ><a name="6219"
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><a name="6221"
> </a
- ><a name="6222" href="Stlc.html#6176" class="Bound"
+ ><a name="6222" href="Stlc.html#3520" class="InductiveConstructor Operator"
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+ ><a name="6224"
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+ ><a name="6225" href="Stlc.html#6179" class="Bound"
>x</a
- ><a name="6223"
+ ><a name="6226"
> </a
- ><a name="6224" href="Stlc.html#3517" class="InductiveConstructor Operator"
+ ><a name="6227" href="Stlc.html#3520" class="InductiveConstructor Operator"
>∶</a
- ><a name="6225"
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> </a
- ><a name="6226" href="Stlc.html#6180" class="Bound"
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>A</a
- ><a name="6227"
+ ><a name="6230"
> </a
- ><a name="6228" href="Stlc.html#3517" class="InductiveConstructor Operator"
+ ><a name="6231" href="Stlc.html#3520" class="InductiveConstructor Operator"
>]</a
- ><a name="6229"
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> </a
- ><a name="6230" href="Stlc.html#6178" class="Bound"
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>N</a
- ><a name="6231"
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> </a
- ><a name="6232" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6235" href="Stlc.html#6070" class="Datatype Operator"
>∶</a
- ><a name="6233"
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> </a
- ><a name="6234" href="Stlc.html#6180" class="Bound"
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>A</a
- ><a name="6235"
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> </a
- ><a name="6236" href="Stlc.html#2550" class="InductiveConstructor Operator"
+ ><a name="6239" href="Stlc.html#2550" class="InductiveConstructor Operator"
>⇒</a
- ><a name="6237"
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> </a
- ><a name="6238" href="Stlc.html#6182" class="Bound"
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>B</a
- ><a name="6239"
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>
</a
- ><a name="6242" href="Stlc.html#6242" class="InductiveConstructor"
+ ><a name="6245" href="Stlc.html#6245" class="InductiveConstructor"
>⇒-E</a
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> </a
- ><a name="6246" class="Symbol"
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>:</a
- ><a name="6247"
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> </a
- ><a name="6248" class="Symbol"
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>∀</a
- ><a name="6249"
- > </a
- ><a name="6250" class="Symbol"
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- ><a name="6251" href="Stlc.html#6251" class="Bound"
- >Γ</a
><a name="6252"
> </a
- ><a name="6253" href="Stlc.html#6253" class="Bound"
+ ><a name="6253" class="Symbol"
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+ ><a name="6254" href="Stlc.html#6254" class="Bound"
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+ ><a name="6255"
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>L</a
- ><a name="6254"
+ ><a name="6257"
> </a
- ><a name="6255" href="Stlc.html#6255" class="Bound"
+ ><a name="6258" href="Stlc.html#6258" class="Bound"
>M</a
- ><a name="6256"
+ ><a name="6259"
> </a
- ><a name="6257" href="Stlc.html#6257" class="Bound"
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>A</a
- ><a name="6258"
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- ><a name="6259" href="Stlc.html#6259" class="Bound"
- >B</a
- ><a name="6260" class="Symbol"
- >}</a
><a name="6261"
> </a
- ><a name="6262" class="Symbol"
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>→</a
- ><a name="6263"
+ ><a name="6266"
>
</a
- ><a name="6268" href="Stlc.html#6251" class="Bound"
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>Γ</a
- ><a name="6269"
+ ><a name="6272"
> </a
- ><a name="6270" href="Stlc.html#6067" class="Datatype Operator"
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>⊢</a
- ><a name="6271"
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> </a
- ><a name="6272" href="Stlc.html#6253" class="Bound"
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>L</a
- ><a name="6273"
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> </a
- ><a name="6274" href="Stlc.html#6067" class="Datatype Operator"
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>∶</a
- ><a name="6275"
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> </a
- ><a name="6276" href="Stlc.html#6257" class="Bound"
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>A</a
- ><a name="6277"
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> </a
- ><a name="6278" href="Stlc.html#2550" class="InductiveConstructor Operator"
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>⇒</a
- ><a name="6279"
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> </a
- ><a name="6280" href="Stlc.html#6259" class="Bound"
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>B</a
- ><a name="6281"
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> </a
- ><a name="6282" class="Symbol"
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>→</a
- ><a name="6283"
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>
</a
- ><a name="6288" href="Stlc.html#6251" class="Bound"
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>Γ</a
- ><a name="6289"
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> </a
- ><a name="6290" href="Stlc.html#6067" class="Datatype Operator"
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>⊢</a
- ><a name="6291"
+ ><a name="6294"
> </a
- ><a name="6292" href="Stlc.html#6255" class="Bound"
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>M</a
- ><a name="6293"
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> </a
- ><a name="6294" href="Stlc.html#6067" class="Datatype Operator"
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>∶</a
- ><a name="6295"
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> </a
- ><a name="6296" href="Stlc.html#6257" class="Bound"
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>A</a
- ><a name="6297"
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> </a
- ><a name="6298" class="Symbol"
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>→</a
- ><a name="6299"
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>
</a
- ><a name="6304" href="Stlc.html#6251" class="Bound"
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>Γ</a
- ><a name="6305"
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> </a
- ><a name="6306" href="Stlc.html#6067" class="Datatype Operator"
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>⊢</a
- ><a name="6307"
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> </a
- ><a name="6308" href="Stlc.html#6253" class="Bound"
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>L</a
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> </a
- ><a name="6310" href="Stlc.html#3553" class="InductiveConstructor Operator"
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- ><a name="6311"
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> </a
- ><a name="6312" href="Stlc.html#6255" class="Bound"
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>M</a
- ><a name="6313"
+ ><a name="6316"
> </a
- ><a name="6314" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6317" href="Stlc.html#6070" class="Datatype Operator"
>∶</a
- ><a name="6315"
+ ><a name="6318"
> </a
- ><a name="6316" href="Stlc.html#6259" class="Bound"
+ ><a name="6319" href="Stlc.html#6262" class="Bound"
>B</a
- ><a name="6317"
+ ><a name="6320"
>
</a
- ><a name="6320" href="Stlc.html#6320" class="InductiveConstructor"
+ ><a name="6323" href="Stlc.html#6323" class="InductiveConstructor"
>𝔹-I₁</a
- ><a name="6324"
+ ><a name="6327"
> </a
- ><a name="6325" class="Symbol"
+ ><a name="6328" class="Symbol"
>:</a
- ><a name="6326"
+ ><a name="6329"
> </a
- ><a name="6327" class="Symbol"
+ ><a name="6330" class="Symbol"
>∀</a
- ><a name="6328"
+ ><a name="6331"
> </a
- ><a name="6329" class="Symbol"
+ ><a name="6332" class="Symbol"
>{</a
- ><a name="6330" href="Stlc.html#6330" class="Bound"
+ ><a name="6333" href="Stlc.html#6333" class="Bound"
>Γ</a
- ><a name="6331" class="Symbol"
+ ><a name="6334" class="Symbol"
>}</a
- ><a name="6332"
+ ><a name="6335"
> </a
- ><a name="6333" class="Symbol"
+ ><a name="6336" class="Symbol"
>→</a
- ><a name="6334"
+ ><a name="6337"
>
</a
- ><a name="6339" href="Stlc.html#6330" class="Bound"
+ ><a name="6342" href="Stlc.html#6333" class="Bound"
>Γ</a
- ><a name="6340"
+ ><a name="6343"
> </a
- ><a name="6341" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6344" href="Stlc.html#6070" class="Datatype Operator"
>⊢</a
- ><a name="6342"
+ ><a name="6345"
> </a
- ><a name="6343" href="Stlc.html#3580" class="InductiveConstructor"
+ ><a name="6346" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
- ><a name="6347"
+ ><a name="6350"
> </a
- ><a name="6348" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6351" href="Stlc.html#6070" class="Datatype Operator"
>∶</a
- ><a name="6349"
+ ><a name="6352"
> </a
- ><a name="6350" href="Stlc.html#2577" class="InductiveConstructor"
+ ><a name="6353" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
- ><a name="6351"
+ ><a name="6354"
>
</a
- ><a name="6354" href="Stlc.html#6354" class="InductiveConstructor"
+ ><a name="6357" href="Stlc.html#6357" class="InductiveConstructor"
>𝔹-I₂</a
- ><a name="6358"
+ ><a name="6361"
> </a
- ><a name="6359" class="Symbol"
+ ><a name="6362" class="Symbol"
>:</a
- ><a name="6360"
+ ><a name="6363"
> </a
- ><a name="6361" class="Symbol"
+ ><a name="6364" class="Symbol"
>∀</a
- ><a name="6362"
+ ><a name="6365"
> </a
- ><a name="6363" class="Symbol"
+ ><a name="6366" class="Symbol"
>{</a
- ><a name="6364" href="Stlc.html#6364" class="Bound"
+ ><a name="6367" href="Stlc.html#6367" class="Bound"
>Γ</a
- ><a name="6365" class="Symbol"
+ ><a name="6368" class="Symbol"
>}</a
- ><a name="6366"
+ ><a name="6369"
> </a
- ><a name="6367" class="Symbol"
+ ><a name="6370" class="Symbol"
>→</a
- ><a name="6368"
+ ><a name="6371"
>
</a
- ><a name="6373" href="Stlc.html#6364" class="Bound"
+ ><a name="6376" href="Stlc.html#6367" class="Bound"
>Γ</a
- ><a name="6374"
+ ><a name="6377"
> </a
- ><a name="6375" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6378" href="Stlc.html#6070" class="Datatype Operator"
>⊢</a
- ><a name="6376"
+ ><a name="6379"
> </a
- ><a name="6377" href="Stlc.html#3594" class="InductiveConstructor"
+ ><a name="6380" href="Stlc.html#3597" class="InductiveConstructor"
>false</a
- ><a name="6382"
+ ><a name="6385"
> </a
- ><a name="6383" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6386" href="Stlc.html#6070" class="Datatype Operator"
>∶</a
- ><a name="6384"
+ ><a name="6387"
> </a
- ><a name="6385" href="Stlc.html#2577" class="InductiveConstructor"
+ ><a name="6388" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
- ><a name="6386"
+ ><a name="6389"
>
</a
- ><a name="6389" href="Stlc.html#6389" class="InductiveConstructor"
+ ><a name="6392" href="Stlc.html#6392" class="InductiveConstructor"
>𝔹-E</a
- ><a name="6392"
+ ><a name="6395"
> </a
- ><a name="6393" class="Symbol"
+ ><a name="6396" class="Symbol"
>:</a
- ><a name="6394"
+ ><a name="6397"
> </a
- ><a name="6395" class="Symbol"
+ ><a name="6398" class="Symbol"
>∀</a
- ><a name="6396"
- > </a
- ><a name="6397" class="Symbol"
- >{</a
- ><a name="6398" href="Stlc.html#6398" class="Bound"
- >Γ</a
><a name="6399"
> </a
- ><a name="6400" href="Stlc.html#6400" class="Bound"
+ ><a name="6400" class="Symbol"
+ >{</a
+ ><a name="6401" href="Stlc.html#6401" class="Bound"
+ >Γ</a
+ ><a name="6402"
+ > </a
+ ><a name="6403" href="Stlc.html#6403" class="Bound"
>L</a
- ><a name="6401"
+ ><a name="6404"
> </a
- ><a name="6402" href="Stlc.html#6402" class="Bound"
+ ><a name="6405" href="Stlc.html#6405" class="Bound"
>M</a
- ><a name="6403"
+ ><a name="6406"
> </a
- ><a name="6404" href="Stlc.html#6404" class="Bound"
+ ><a name="6407" href="Stlc.html#6407" class="Bound"
>N</a
- ><a name="6405"
- > </a
- ><a name="6406" href="Stlc.html#6406" class="Bound"
- >A</a
- ><a name="6407" class="Symbol"
- >}</a
><a name="6408"
> </a
- ><a name="6409" class="Symbol"
+ ><a name="6409" href="Stlc.html#6409" class="Bound"
+ >A</a
+ ><a name="6410" class="Symbol"
+ >}</a
+ ><a name="6411"
+ > </a
+ ><a name="6412" class="Symbol"
>→</a
- ><a name="6410"
+ ><a name="6413"
>
</a
- ><a name="6415" href="Stlc.html#6398" class="Bound"
+ ><a name="6418" href="Stlc.html#6401" class="Bound"
>Γ</a
- ><a name="6416"
+ ><a name="6419"
> </a
- ><a name="6417" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6420" href="Stlc.html#6070" class="Datatype Operator"
>⊢</a
- ><a name="6418"
+ ><a name="6421"
> </a
- ><a name="6419" href="Stlc.html#6400" class="Bound"
+ ><a name="6422" href="Stlc.html#6403" class="Bound"
>L</a
- ><a name="6420"
+ ><a name="6423"
> </a
- ><a name="6421" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6424" href="Stlc.html#6070" class="Datatype Operator"
>∶</a
- ><a name="6422"
+ ><a name="6425"
> </a
- ><a name="6423" href="Stlc.html#2577" class="InductiveConstructor"
+ ><a name="6426" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
- ><a name="6424"
+ ><a name="6427"
> </a
- ><a name="6425" class="Symbol"
+ ><a name="6428" class="Symbol"
>→</a
- ><a name="6426"
+ ><a name="6429"
>
</a
- ><a name="6431" href="Stlc.html#6398" class="Bound"
+ ><a name="6434" href="Stlc.html#6401" class="Bound"
>Γ</a
- ><a name="6432"
+ ><a name="6435"
> </a
- ><a name="6433" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6436" href="Stlc.html#6070" class="Datatype Operator"
>⊢</a
- ><a name="6434"
+ ><a name="6437"
> </a
- ><a name="6435" href="Stlc.html#6402" class="Bound"
+ ><a name="6438" href="Stlc.html#6405" class="Bound"
>M</a
- ><a name="6436"
+ ><a name="6439"
> </a
- ><a name="6437" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6440" href="Stlc.html#6070" class="Datatype Operator"
>∶</a
- ><a name="6438"
+ ><a name="6441"
> </a
- ><a name="6439" href="Stlc.html#6406" class="Bound"
+ ><a name="6442" href="Stlc.html#6409" class="Bound"
>A</a
- ><a name="6440"
+ ><a name="6443"
> </a
- ><a name="6441" class="Symbol"
+ ><a name="6444" class="Symbol"
>→</a
- ><a name="6442"
+ ><a name="6445"
>
</a
- ><a name="6447" href="Stlc.html#6398" class="Bound"
+ ><a name="6450" href="Stlc.html#6401" class="Bound"
>Γ</a
- ><a name="6448"
+ ><a name="6451"
> </a
- ><a name="6449" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6452" href="Stlc.html#6070" class="Datatype Operator"
>⊢</a
- ><a name="6450"
+ ><a name="6453"
> </a
- ><a name="6451" href="Stlc.html#6404" class="Bound"
+ ><a name="6454" href="Stlc.html#6407" class="Bound"
>N</a
- ><a name="6452"
+ ><a name="6455"
> </a
- ><a name="6453" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6456" href="Stlc.html#6070" class="Datatype Operator"
>∶</a
- ><a name="6454"
+ ><a name="6457"
> </a
- ><a name="6455" href="Stlc.html#6406" class="Bound"
+ ><a name="6458" href="Stlc.html#6409" class="Bound"
>A</a
- ><a name="6456"
+ ><a name="6459"
> </a
- ><a name="6457" class="Symbol"
+ ><a name="6460" class="Symbol"
>→</a
- ><a name="6458"
+ ><a name="6461"
>
</a
- ><a name="6463" href="Stlc.html#6398" class="Bound"
+ ><a name="6466" href="Stlc.html#6401" class="Bound"
>Γ</a
- ><a name="6464"
+ ><a name="6467"
> </a
- ><a name="6465" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6468" href="Stlc.html#6070" class="Datatype Operator"
>⊢</a
- ><a name="6466"
- > </a
- ><a name="6467" href="Stlc.html#3609" class="InductiveConstructor Operator"
- >if</a
><a name="6469"
> </a
- ><a name="6470" href="Stlc.html#6400" class="Bound"
+ ><a name="6470" href="Stlc.html#3612" class="InductiveConstructor Operator"
+ >if</a
+ ><a name="6472"
+ > </a
+ ><a name="6473" href="Stlc.html#6403" class="Bound"
>L</a
- ><a name="6471"
+ ><a name="6474"
> </a
- ><a name="6472" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="6475" href="Stlc.html#3612" class="InductiveConstructor Operator"
>then</a
- ><a name="6476"
+ ><a name="6479"
> </a
- ><a name="6477" href="Stlc.html#6402" class="Bound"
+ ><a name="6480" href="Stlc.html#6405" class="Bound"
>M</a
- ><a name="6478"
+ ><a name="6481"
> </a
- ><a name="6479" href="Stlc.html#3609" class="InductiveConstructor Operator"
+ ><a name="6482" href="Stlc.html#3612" class="InductiveConstructor Operator"
>else</a
- ><a name="6483"
+ ><a name="6486"
> </a
- ><a name="6484" href="Stlc.html#6404" class="Bound"
+ ><a name="6487" href="Stlc.html#6407" class="Bound"
>N</a
- ><a name="6485"
+ ><a name="6488"
> </a
- ><a name="6486" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6489" href="Stlc.html#6070" class="Datatype Operator"
>∶</a
- ><a name="6487"
+ ><a name="6490"
> </a
- ><a name="6488" href="Stlc.html#6406" class="Bound"
+ ><a name="6491" href="Stlc.html#6409" class="Bound"
>A</a
>
@@ -3553,205 +3553,205 @@ Much of the above, though not all, can be filled in using C-c C-r and C-c C-s.
<pre class="Agda">
-<a name="6548" href="Stlc.html#6548" class="Function"
+<a name="6551" href="Stlc.html#6551" class="Function"
>typing₁</a
- ><a name="6555"
+ ><a name="6558"
> </a
- ><a name="6556" class="Symbol"
+ ><a name="6559" class="Symbol"
>:</a
- ><a name="6557"
+ ><a name="6560"
> </a
- ><a name="6558" href="Maps.html#10265" class="Function"
+ ><a name="6561" href="Maps.html#10265" class="Function"
>∅</a
- ><a name="6559"
+ ><a name="6562"
> </a
- ><a name="6560" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6563" href="Stlc.html#6070" class="Datatype Operator"
>⊢</a
- ><a name="6561"
+ ><a name="6564"
> </a
- ><a name="6562" href="Stlc.html#3904" class="Function"
+ ><a name="6565" href="Stlc.html#3907" class="Function"
>not</a
- ><a name="6565"
+ ><a name="6568"
> </a
- ><a name="6566" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6569" href="Stlc.html#6070" class="Datatype Operator"
>∶</a
- ><a name="6567"
+ ><a name="6570"
> </a
- ><a name="6568" href="Stlc.html#2577" class="InductiveConstructor"
+ ><a name="6571" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
- ><a name="6569"
+ ><a name="6572"
> </a
- ><a name="6570" href="Stlc.html#2550" class="InductiveConstructor Operator"
+ ><a name="6573" href="Stlc.html#2550" class="InductiveConstructor Operator"
>⇒</a
- ><a name="6571"
+ ><a name="6574"
> </a
- ><a name="6572" href="Stlc.html#2577" class="InductiveConstructor"
+ ><a name="6575" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
- ><a name="6573"
+ ><a name="6576"
>
</a
- ><a name="6574" href="Stlc.html#6548" class="Function"
+ ><a name="6577" href="Stlc.html#6551" class="Function"
>typing₁</a
- ><a name="6581"
+ ><a name="6584"
> </a
- ><a name="6582" class="Symbol"
+ ><a name="6585" class="Symbol"
>=</a
- ><a name="6583"
+ ><a name="6586"
> </a
- ><a name="6584" href="Stlc.html#6165" class="InductiveConstructor"
+ ><a name="6587" href="Stlc.html#6168" class="InductiveConstructor"
>⇒-I</a
- ><a name="6587"
+ ><a name="6590"
> </a
- ><a name="6588" class="Symbol"
+ ><a name="6591" class="Symbol"
>(</a
- ><a name="6589" href="Stlc.html#6389" class="InductiveConstructor"
+ ><a name="6592" href="Stlc.html#6392" class="InductiveConstructor"
>𝔹-E</a
- ><a name="6592"
+ ><a name="6595"
> </a
- ><a name="6593" class="Symbol"
+ ><a name="6596" class="Symbol"
>(</a
- ><a name="6594" href="Stlc.html#6111" class="InductiveConstructor"
+ ><a name="6597" href="Stlc.html#6114" class="InductiveConstructor"
>Ax</a
- ><a name="6596"
+ ><a name="6599"
> </a
- ><a name="6597" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#140" class="InductiveConstructor"
+ ><a name="6600" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#140" class="InductiveConstructor"
>refl</a
- ><a name="6601" class="Symbol"
+ ><a name="6604" class="Symbol"
>)</a
- ><a name="6602"
+ ><a name="6605"
> </a
- ><a name="6603" href="Stlc.html#6354" class="InductiveConstructor"
+ ><a name="6606" href="Stlc.html#6357" class="InductiveConstructor"
>𝔹-I₂</a
- ><a name="6607"
+ ><a name="6610"
> </a
- ><a name="6608" href="Stlc.html#6320" class="InductiveConstructor"
+ ><a name="6611" href="Stlc.html#6323" class="InductiveConstructor"
>𝔹-I₁</a
- ><a name="6612" class="Symbol"
+ ><a name="6615" class="Symbol"
>)</a
- ><a name="6613"
+ ><a name="6616"
>
</a
- ><a name="6615" href="Stlc.html#6615" class="Function"
+ ><a name="6618" href="Stlc.html#6618" class="Function"
>typing₂</a
- ><a name="6622"
+ ><a name="6625"
> </a
- ><a name="6623" class="Symbol"
+ ><a name="6626" class="Symbol"
>:</a
- ><a name="6624"
+ ><a name="6627"
> </a
- ><a name="6625" href="Maps.html#10265" class="Function"
+ ><a name="6628" href="Maps.html#10265" class="Function"
>∅</a
- ><a name="6626"
+ ><a name="6629"
> </a
- ><a name="6627" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6630" href="Stlc.html#6070" class="Datatype Operator"
>⊢</a
- ><a name="6628"
+ ><a name="6631"
> </a
- ><a name="6629" href="Stlc.html#3908" class="Function"
+ ><a name="6632" href="Stlc.html#3911" class="Function"
>two</a
- ><a name="6632"
+ ><a name="6635"
> </a
- ><a name="6633" href="Stlc.html#6067" class="Datatype Operator"
+ ><a name="6636" href="Stlc.html#6070" class="Datatype Operator"
>∶</a
- ><a name="6634"
- > </a
- ><a name="6635" class="Symbol"
- >(</a
- ><a name="6636" href="Stlc.html#2577" class="InductiveConstructor"
- >𝔹</a
><a name="6637"
> </a
- ><a name="6638" href="Stlc.html#2550" class="InductiveConstructor Operator"
- >⇒</a
- ><a name="6639"
- > </a
- ><a name="6640" href="Stlc.html#2577" class="InductiveConstructor"
+ ><a name="6638" class="Symbol"
+ >(</a
+ ><a name="6639" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
- ><a name="6641" class="Symbol"
- >)</a
+ ><a name="6640"
+ > </a
+ ><a name="6641" href="Stlc.html#2550" class="InductiveConstructor Operator"
+ >⇒</a
><a name="6642"
> </a
- ><a name="6643" href="Stlc.html#2550" class="InductiveConstructor Operator"
- >⇒</a
- ><a name="6644"
- > </a
- ><a name="6645" href="Stlc.html#2577" class="InductiveConstructor"
+ ><a name="6643" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
- ><a name="6646"
+ ><a name="6644" class="Symbol"
+ >)</a
+ ><a name="6645"
> </a
- ><a name="6647" href="Stlc.html#2550" class="InductiveConstructor Operator"
+ ><a name="6646" href="Stlc.html#2550" class="InductiveConstructor Operator"
>⇒</a
- ><a name="6648"
+ ><a name="6647"
> </a
- ><a name="6649" href="Stlc.html#2577" class="InductiveConstructor"
+ ><a name="6648" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
- ><a name="6650"
+ ><a name="6649"
+ > </a
+ ><a name="6650" href="Stlc.html#2550" class="InductiveConstructor Operator"
+ >⇒</a
+ ><a name="6651"
+ > </a
+ ><a name="6652" href="Stlc.html#2577" class="InductiveConstructor"
+ >𝔹</a
+ ><a name="6653"
>
</a
- ><a name="6651" href="Stlc.html#6615" class="Function"
+ ><a name="6654" href="Stlc.html#6618" class="Function"
>typing₂</a
- ><a name="6658"
+ ><a name="6661"
> </a
- ><a name="6659" class="Symbol"
+ ><a name="6662" class="Symbol"
>=</a
- ><a name="6660"
+ ><a name="6663"
> </a
- ><a name="6661" href="Stlc.html#6165" class="InductiveConstructor"
+ ><a name="6664" href="Stlc.html#6168" class="InductiveConstructor"
>⇒-I</a
- ><a name="6664"
+ ><a name="6667"
> </a
- ><a name="6665" class="Symbol"
+ ><a name="6668" class="Symbol"
>(</a
- ><a name="6666" href="Stlc.html#6165" class="InductiveConstructor"
+ ><a name="6669" href="Stlc.html#6168" class="InductiveConstructor"
>⇒-I</a
- ><a name="6669"
+ ><a name="6672"
> </a
- ><a name="6670" class="Symbol"
+ ><a name="6673" class="Symbol"
>(</a
- ><a name="6671" href="Stlc.html#6242" class="InductiveConstructor"
+ ><a name="6674" href="Stlc.html#6245" class="InductiveConstructor"
>⇒-E</a
- ><a name="6674"
+ ><a name="6677"
> </a
- ><a name="6675" class="Symbol"
+ ><a name="6678" class="Symbol"
>(</a
- ><a name="6676" href="Stlc.html#6111" class="InductiveConstructor"
+ ><a name="6679" href="Stlc.html#6114" class="InductiveConstructor"
>Ax</a
- ><a name="6678"
+ ><a name="6681"
> </a
- ><a name="6679" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#140" class="InductiveConstructor"
+ ><a name="6682" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#140" class="InductiveConstructor"
>refl</a
- ><a name="6683" class="Symbol"
+ ><a name="6686" class="Symbol"
>)</a
- ><a name="6684"
+ ><a name="6687"
> </a
- ><a name="6685" class="Symbol"
+ ><a name="6688" class="Symbol"
>(</a
- ><a name="6686" href="Stlc.html#6242" class="InductiveConstructor"
+ ><a name="6689" href="Stlc.html#6245" class="InductiveConstructor"
>⇒-E</a
- ><a name="6689"
+ ><a name="6692"
> </a
- ><a name="6690" class="Symbol"
+ ><a name="6693" class="Symbol"
>(</a
- ><a name="6691" href="Stlc.html#6111" class="InductiveConstructor"
+ ><a name="6694" href="Stlc.html#6114" class="InductiveConstructor"
>Ax</a
- ><a name="6693"
+ ><a name="6696"
> </a
- ><a name="6694" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#140" class="InductiveConstructor"
+ ><a name="6697" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#140" class="InductiveConstructor"
>refl</a
- ><a name="6698" class="Symbol"
+ ><a name="6701" class="Symbol"
>)</a
- ><a name="6699"
+ ><a name="6702"
> </a
- ><a name="6700" class="Symbol"
+ ><a name="6703" class="Symbol"
>(</a
- ><a name="6701" href="Stlc.html#6111" class="InductiveConstructor"
+ ><a name="6704" href="Stlc.html#6114" class="InductiveConstructor"
>Ax</a
- ><a name="6703"
+ ><a name="6706"
> </a
- ><a name="6704" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#140" class="InductiveConstructor"
+ ><a name="6707" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#140" class="InductiveConstructor"
>refl</a
- ><a name="6708" class="Symbol"
+ ><a name="6711" class="Symbol"
>))))</a
>
@@ -3785,7 +3785,7 @@ outermost term is now `if_then_else_`, which is typed using `𝔹-E`. The
?2 : ∅ , x ∶ 𝔹 ⊢ true ∶ 𝔹
Again we fill in the three holes by typing C-c C-r in each. Agda observes
-that `\` x`, `false`, and `true` are typed using `Ax`, `𝔹-I₂`, and
+that `` ` x ``, `false`, and `true` are typed using `Ax`, `𝔹-I₂`, and
`𝔹-I₁` respectively. The `Ax` rule in turn takes an argument, to show
that `(∅ , x ∶ 𝔹) x = just 𝔹`, which can in turn be specified with a
hole. After filling in all holes, the term is as above.
diff --git a/out/StlcProp.md b/out/StlcProp.md
index 54616b83..86a1c3bc 100644
--- a/out/StlcProp.md
+++ b/out/StlcProp.md
@@ -433,7 +433,7 @@ while for boolean types they are values `true` and `false`.
>:</a
><a name="1234"
> </a
- ><a name="1235" href="Stlc.html#708" class="Datatype"
+ ><a name="1235" href="Stlc.html#3485" class="Datatype"
>Term</a
><a name="1239"
> </a
@@ -441,7 +441,7 @@ while for boolean types they are values `true` and `false`.
>→</a
><a name="1241"
> </a
- ><a name="1242" href="Stlc.html#590" class="Datatype"
+ ><a name="1242" href="Stlc.html#2531" class="Datatype"
>Type</a
><a name="1246"
> </a
@@ -500,7 +500,7 @@ while for boolean types they are values `true` and `false`.
> </a
><a name="1299" class="Symbol"
>(</a
- ><a name="1300" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="1300" href="Stlc.html#3520" class="InductiveConstructor Operator"
>λ[</a
><a name="1302"
> </a
@@ -508,7 +508,7 @@ while for boolean types they are values `true` and `false`.
>x</a
><a name="1304"
> </a
- ><a name="1305" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="1305" href="Stlc.html#3520" class="InductiveConstructor Operator"
>∶</a
><a name="1306"
> </a
@@ -516,7 +516,7 @@ while for boolean types they are values `true` and `false`.
>A</a
><a name="1308"
> </a
- ><a name="1309" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="1309" href="Stlc.html#3520" class="InductiveConstructor Operator"
>]</a
><a name="1310"
> </a
@@ -536,7 +536,7 @@ while for boolean types they are values `true` and `false`.
>A</a
><a name="1320"
> </a
- ><a name="1321" href="Stlc.html#609" class="InductiveConstructor Operator"
+ ><a name="1321" href="Stlc.html#2550" class="InductiveConstructor Operator"
>⇒</a
><a name="1322"
> </a
@@ -559,7 +559,7 @@ while for boolean types they are values `true` and `false`.
>canonical</a
><a name="1354"
> </a
- ><a name="1355" href="Stlc.html#806" class="InductiveConstructor"
+ ><a name="1355" href="Stlc.html#3583" class="InductiveConstructor"
>true</a
><a name="1359"
> </a
@@ -567,7 +567,7 @@ while for boolean types they are values `true` and `false`.
>for</a
><a name="1363"
> </a
- ><a name="1364" href="Stlc.html#636" class="InductiveConstructor"
+ ><a name="1364" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
><a name="1365"
>
@@ -584,7 +584,7 @@ while for boolean types they are values `true` and `false`.
>canonical</a
><a name="1395"
> </a
- ><a name="1396" href="Stlc.html#820" class="InductiveConstructor"
+ ><a name="1396" href="Stlc.html#3597" class="InductiveConstructor"
>false</a
><a name="1401"
> </a
@@ -592,7 +592,7 @@ while for boolean types they are values `true` and `false`.
>for</a
><a name="1405"
> </a
- ><a name="1406" href="Stlc.html#636" class="InductiveConstructor"
+ ><a name="1406" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
><a name="1407"
>
@@ -630,7 +630,7 @@ while for boolean types they are values `true` and `false`.
>∅</a
><a name="1438"
> </a
- ><a name="1439" href="Stlc.html#3112" class="Datatype Operator"
+ ><a name="1439" href="Stlc.html#6070" class="Datatype Operator"
>⊢</a
><a name="1440"
> </a
@@ -638,7 +638,7 @@ while for boolean types they are values `true` and `false`.
>L</a
><a name="1442"
> </a
- ><a name="1443" href="Stlc.html#3112" class="Datatype Operator"
+ ><a name="1443" href="Stlc.html#6070" class="Datatype Operator"
>∶</a
><a name="1444"
> </a
@@ -650,7 +650,7 @@ while for boolean types they are values `true` and `false`.
>→</a
><a name="1448"
> </a
- ><a name="1449" href="Stlc.html#1105" class="Datatype"
+ ><a name="1449" href="Stlc.html#4063" class="Datatype"
>Value</a
><a name="1454"
> </a
@@ -685,7 +685,7 @@ while for boolean types they are values `true` and `false`.
> </a
><a name="1493" class="Symbol"
>(</a
- ><a name="1494" href="Stlc.html#3156" class="InductiveConstructor"
+ ><a name="1494" href="Stlc.html#6114" class="InductiveConstructor"
>Ax</a
><a name="1496"
> </a
@@ -704,7 +704,7 @@ while for boolean types they are values `true` and `false`.
> </a
><a name="1520" class="Symbol"
>(</a
- ><a name="1521" href="Stlc.html#3210" class="InductiveConstructor"
+ ><a name="1521" href="Stlc.html#6168" class="InductiveConstructor"
>⇒-I</a
><a name="1524"
> </a
@@ -714,7 +714,7 @@ while for boolean types they are values `true` and `false`.
>)</a
><a name="1528"
> </a
- ><a name="1529" href="Stlc.html#1132" class="InductiveConstructor"
+ ><a name="1529" href="Stlc.html#4090" class="InductiveConstructor"
>value-λ</a
><a name="1536"
> </a
@@ -733,7 +733,7 @@ while for boolean types they are values `true` and `false`.
> </a
><a name="1567" class="Symbol"
>(</a
- ><a name="1568" href="Stlc.html#3287" class="InductiveConstructor"
+ ><a name="1568" href="Stlc.html#6245" class="InductiveConstructor"
>⇒-E</a
><a name="1571"
> </a
@@ -756,11 +756,11 @@ while for boolean types they are values `true` and `false`.
>canonical-forms</a
><a name="1597"
> </a
- ><a name="1598" href="Stlc.html#3365" class="InductiveConstructor"
+ ><a name="1598" href="Stlc.html#6323" class="InductiveConstructor"
>𝔹-I₁</a
><a name="1602"
> </a
- ><a name="1603" href="Stlc.html#1181" class="InductiveConstructor"
+ ><a name="1603" href="Stlc.html#4139" class="InductiveConstructor"
>value-true</a
><a name="1613"
> </a
@@ -777,11 +777,11 @@ while for boolean types they are values `true` and `false`.
>canonical-forms</a
><a name="1646"
> </a
- ><a name="1647" href="Stlc.html#3399" class="InductiveConstructor"
+ ><a name="1647" href="Stlc.html#6357" class="InductiveConstructor"
>𝔹-I₂</a
><a name="1651"
> </a
- ><a name="1652" href="Stlc.html#1208" class="InductiveConstructor"
+ ><a name="1652" href="Stlc.html#4166" class="InductiveConstructor"
>value-false</a
><a name="1663"
> </a
@@ -800,7 +800,7 @@ while for boolean types they are values `true` and `false`.
> </a
><a name="1698" class="Symbol"
>(</a
- ><a name="1699" href="Stlc.html#3434" class="InductiveConstructor"
+ ><a name="1699" href="Stlc.html#6392" class="InductiveConstructor"
>𝔹-E</a
><a name="1702"
> </a
@@ -844,7 +844,7 @@ step or it is a value.
>:</a
><a name="1927"
> </a
- ><a name="1928" href="Stlc.html#708" class="Datatype"
+ ><a name="1928" href="Stlc.html#3485" class="Datatype"
>Term</a
><a name="1932"
> </a
@@ -893,7 +893,7 @@ step or it is a value.
>M</a
><a name="1966"
> </a
- ><a name="1967" href="Stlc.html#1762" class="Datatype Operator"
+ ><a name="1967" href="Stlc.html#4720" class="Datatype Operator"
>⟹</a
><a name="1968"
> </a
@@ -938,7 +938,7 @@ step or it is a value.
>→</a
><a name="2001"
> </a
- ><a name="2002" href="Stlc.html#1105" class="Datatype"
+ ><a name="2002" href="Stlc.html#4063" class="Datatype"
>Value</a
><a name="2007"
> </a
@@ -992,7 +992,7 @@ step or it is a value.
>∅</a
><a name="2046"
> </a
- ><a name="2047" href="Stlc.html#3112" class="Datatype Operator"
+ ><a name="2047" href="Stlc.html#6070" class="Datatype Operator"
>⊢</a
><a name="2048"
> </a
@@ -1000,7 +1000,7 @@ step or it is a value.
>M</a
><a name="2050"
> </a
- ><a name="2051" href="Stlc.html#3112" class="Datatype Operator"
+ ><a name="2051" href="Stlc.html#6070" class="Datatype Operator"
>∶</a
><a name="2052"
> </a
@@ -1079,7 +1079,7 @@ This completes the proof.
> </a
><a name="3955" class="Symbol"
>(</a
- ><a name="3956" href="Stlc.html#3156" class="InductiveConstructor"
+ ><a name="3956" href="Stlc.html#6114" class="InductiveConstructor"
>Ax</a
><a name="3958"
> </a
@@ -1094,7 +1094,7 @@ This completes the proof.
> </a
><a name="3972" class="Symbol"
>(</a
- ><a name="3973" href="Stlc.html#3210" class="InductiveConstructor"
+ ><a name="3973" href="Stlc.html#6168" class="InductiveConstructor"
>⇒-I</a
><a name="3976"
> </a
@@ -1112,7 +1112,7 @@ This completes the proof.
>done</a
><a name="3987"
> </a
- ><a name="3988" href="Stlc.html#1132" class="InductiveConstructor"
+ ><a name="3988" href="Stlc.html#4090" class="InductiveConstructor"
>value-λ</a
><a name="3995"
>
@@ -1123,7 +1123,7 @@ This completes the proof.
> </a
><a name="4005" class="Symbol"
>(</a
- ><a name="4006" href="Stlc.html#3287" class="InductiveConstructor"
+ ><a name="4006" href="Stlc.html#6245" class="InductiveConstructor"
>⇒-E</a
><a name="4009"
> </a
@@ -1176,7 +1176,7 @@ This completes the proof.
> </a
><a name="4059" class="Symbol"
>(</a
- ><a name="4060" href="Stlc.html#1864" class="InductiveConstructor"
+ ><a name="4060" href="Stlc.html#4822" class="InductiveConstructor"
>ξ·₁</a
><a name="4063"
> </a
@@ -1242,7 +1242,7 @@ This completes the proof.
> </a
><a name="4130" class="Symbol"
>(</a
- ><a name="4131" href="Stlc.html#1917" class="InductiveConstructor"
+ ><a name="4131" href="Stlc.html#4875" class="InductiveConstructor"
>ξ·₂</a
><a name="4134"
> </a
@@ -1312,7 +1312,7 @@ This completes the proof.
> </a
><a name="4223" class="Symbol"
>(</a
- ><a name="4224" href="Stlc.html#1794" class="InductiveConstructor"
+ ><a name="4224" href="Stlc.html#4752" class="InductiveConstructor"
>βλ·</a
><a name="4227"
> </a
@@ -1327,7 +1327,7 @@ This completes the proof.
>progress</a
><a name="4244"
> </a
- ><a name="4245" href="Stlc.html#3365" class="InductiveConstructor"
+ ><a name="4245" href="Stlc.html#6323" class="InductiveConstructor"
>𝔹-I₁</a
><a name="4249"
> </a
@@ -1339,7 +1339,7 @@ This completes the proof.
>done</a
><a name="4256"
> </a
- ><a name="4257" href="Stlc.html#1181" class="InductiveConstructor"
+ ><a name="4257" href="Stlc.html#4139" class="InductiveConstructor"
>value-true</a
><a name="4267"
>
@@ -1348,7 +1348,7 @@ This completes the proof.
>progress</a
><a name="4276"
> </a
- ><a name="4277" href="Stlc.html#3399" class="InductiveConstructor"
+ ><a name="4277" href="Stlc.html#6357" class="InductiveConstructor"
>𝔹-I₂</a
><a name="4281"
> </a
@@ -1360,7 +1360,7 @@ This completes the proof.
>done</a
><a name="4288"
> </a
- ><a name="4289" href="Stlc.html#1208" class="InductiveConstructor"
+ ><a name="4289" href="Stlc.html#4166" class="InductiveConstructor"
>value-false</a
><a name="4300"
>
@@ -1371,7 +1371,7 @@ This completes the proof.
> </a
><a name="4310" class="Symbol"
>(</a
- ><a name="4311" href="Stlc.html#3434" class="InductiveConstructor"
+ ><a name="4311" href="Stlc.html#6392" class="InductiveConstructor"
>𝔹-E</a
><a name="4314"
> </a
@@ -1428,7 +1428,7 @@ This completes the proof.
> </a
><a name="4367" class="Symbol"
>(</a
- ><a name="4368" href="Stlc.html#2092" class="InductiveConstructor"
+ ><a name="4368" href="Stlc.html#5050" class="InductiveConstructor"
>ξif</a
><a name="4371"
> </a
@@ -1492,7 +1492,7 @@ This completes the proof.
>steps</a
><a name="4455"
> </a
- ><a name="4456" href="Stlc.html#1984" class="InductiveConstructor"
+ ><a name="4456" href="Stlc.html#4942" class="InductiveConstructor"
>βif-true</a
><a name="4464"
>
@@ -1517,7 +1517,7 @@ This completes the proof.
>steps</a
><a name="4494"
> </a
- ><a name="4495" href="Stlc.html#2037" class="InductiveConstructor"
+ ><a name="4495" href="Stlc.html#4995" class="InductiveConstructor"
>βif-false</a
>
@@ -1575,7 +1575,7 @@ instead of induction on typing derivations.
>∅</a
><a name="5187"
> </a
- ><a name="5188" href="Stlc.html#3112" class="Datatype Operator"
+ ><a name="5188" href="Stlc.html#6070" class="Datatype Operator"
>⊢</a
><a name="5189"
> </a
@@ -1583,7 +1583,7 @@ instead of induction on typing derivations.
>M</a
><a name="5191"
> </a
- ><a name="5192" href="Stlc.html#3112" class="Datatype Operator"
+ ><a name="5192" href="Stlc.html#6070" class="Datatype Operator"
>∶</a
><a name="5193"
> </a
@@ -1681,7 +1681,7 @@ Formally:
>→</a
><a name="7669"
> </a
- ><a name="7670" href="Stlc.html#708" class="Datatype"
+ ><a name="7670" href="Stlc.html#3485" class="Datatype"
>Term</a
><a name="7674"
> </a
@@ -1730,7 +1730,7 @@ Formally:
>∈</a
><a name="7710"
> </a
- ><a name="7711" href="Stlc.html#727" class="InductiveConstructor"
+ ><a name="7711" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
><a name="7712"
> </a
@@ -1817,7 +1817,7 @@ Formally:
> </a
><a name="7761" class="Symbol"
>(</a
- ><a name="7762" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="7762" href="Stlc.html#3520" class="InductiveConstructor Operator"
>λ[</a
><a name="7764"
> </a
@@ -1825,7 +1825,7 @@ Formally:
>y</a
><a name="7766"
> </a
- ><a name="7767" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="7767" href="Stlc.html#3520" class="InductiveConstructor Operator"
>∶</a
><a name="7768"
> </a
@@ -1833,7 +1833,7 @@ Formally:
>A</a
><a name="7770"
> </a
- ><a name="7771" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="7771" href="Stlc.html#3520" class="InductiveConstructor Operator"
>]</a
><a name="7772"
> </a
@@ -1906,7 +1906,7 @@ Formally:
>L</a
><a name="7814"
> </a
- ><a name="7815" href="Stlc.html#779" class="InductiveConstructor Operator"
+ ><a name="7815" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
><a name="7816"
> </a
@@ -1979,7 +1979,7 @@ Formally:
>L</a
><a name="7858"
> </a
- ><a name="7859" href="Stlc.html#779" class="InductiveConstructor Operator"
+ ><a name="7859" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
><a name="7860"
> </a
@@ -2052,7 +2052,7 @@ Formally:
> </a
><a name="7903" class="Symbol"
>(</a
- ><a name="7904" href="Stlc.html#835" class="InductiveConstructor Operator"
+ ><a name="7904" href="Stlc.html#3612" class="InductiveConstructor Operator"
>if</a
><a name="7906"
> </a
@@ -2060,7 +2060,7 @@ Formally:
>L</a
><a name="7908"
> </a
- ><a name="7909" href="Stlc.html#835" class="InductiveConstructor Operator"
+ ><a name="7909" href="Stlc.html#3612" class="InductiveConstructor Operator"
>then</a
><a name="7913"
> </a
@@ -2068,7 +2068,7 @@ Formally:
>M</a
><a name="7915"
> </a
- ><a name="7916" href="Stlc.html#835" class="InductiveConstructor Operator"
+ ><a name="7916" href="Stlc.html#3612" class="InductiveConstructor Operator"
>else</a
><a name="7920"
> </a
@@ -2141,7 +2141,7 @@ Formally:
> </a
><a name="7963" class="Symbol"
>(</a
- ><a name="7964" href="Stlc.html#835" class="InductiveConstructor Operator"
+ ><a name="7964" href="Stlc.html#3612" class="InductiveConstructor Operator"
>if</a
><a name="7966"
> </a
@@ -2149,7 +2149,7 @@ Formally:
>L</a
><a name="7968"
> </a
- ><a name="7969" href="Stlc.html#835" class="InductiveConstructor Operator"
+ ><a name="7969" href="Stlc.html#3612" class="InductiveConstructor Operator"
>then</a
><a name="7973"
> </a
@@ -2157,7 +2157,7 @@ Formally:
>M</a
><a name="7975"
> </a
- ><a name="7976" href="Stlc.html#835" class="InductiveConstructor Operator"
+ ><a name="7976" href="Stlc.html#3612" class="InductiveConstructor Operator"
>else</a
><a name="7980"
> </a
@@ -2230,7 +2230,7 @@ Formally:
> </a
><a name="8023" class="Symbol"
>(</a
- ><a name="8024" href="Stlc.html#835" class="InductiveConstructor Operator"
+ ><a name="8024" href="Stlc.html#3612" class="InductiveConstructor Operator"
>if</a
><a name="8026"
> </a
@@ -2238,7 +2238,7 @@ Formally:
>L</a
><a name="8028"
> </a
- ><a name="8029" href="Stlc.html#835" class="InductiveConstructor Operator"
+ ><a name="8029" href="Stlc.html#3612" class="InductiveConstructor Operator"
>then</a
><a name="8033"
> </a
@@ -2246,7 +2246,7 @@ Formally:
>M</a
><a name="8035"
> </a
- ><a name="8036" href="Stlc.html#835" class="InductiveConstructor Operator"
+ ><a name="8036" href="Stlc.html#3612" class="InductiveConstructor Operator"
>else</a
><a name="8040"
> </a
@@ -2278,7 +2278,7 @@ A term in which no variables appear free is said to be _closed_.
>→</a
><a name="8145"
> </a
- ><a name="8146" href="Stlc.html#708" class="Datatype"
+ ><a name="8146" href="Stlc.html#3485" class="Datatype"
>Term</a
><a name="8150"
> </a
@@ -2337,7 +2337,7 @@ A term in which no variables appear free is said to be _closed_.
>:</a
><a name="8184"
> </a
- ><a name="8185" href="Stlc.html#708" class="Datatype"
+ ><a name="8185" href="Stlc.html#3485" class="Datatype"
>Term</a
><a name="8189"
> </a
@@ -2404,7 +2404,7 @@ Here are proofs corresponding to the first two examples above.
>:</a
><a name="8315"
> </a
- ><a name="8316" href="Stlc.html#917" class="Function"
+ ><a name="8316" href="Stlc.html#3875" class="Function"
>f</a
><a name="8317"
> </a
@@ -2412,7 +2412,7 @@ Here are proofs corresponding to the first two examples above.
>≢</a
><a name="8319"
> </a
- ><a name="8320" href="Stlc.html#919" class="Function"
+ ><a name="8320" href="Stlc.html#3877" class="Function"
>x</a
><a name="8321"
>
@@ -2435,7 +2435,7 @@ Here are proofs corresponding to the first two examples above.
>:</a
><a name="8345"
> </a
- ><a name="8346" href="Stlc.html#919" class="Function"
+ ><a name="8346" href="Stlc.html#3877" class="Function"
>x</a
><a name="8347"
> </a
@@ -2445,55 +2445,55 @@ Here are proofs corresponding to the first two examples above.
> </a
><a name="8350" class="Symbol"
>(</a
- ><a name="8351" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8351" href="Stlc.html#3520" class="InductiveConstructor Operator"
>λ[</a
><a name="8353"
> </a
- ><a name="8354" href="Stlc.html#917" class="Function"
+ ><a name="8354" href="Stlc.html#3875" class="Function"
>f</a
><a name="8355"
> </a
- ><a name="8356" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8356" href="Stlc.html#3520" class="InductiveConstructor Operator"
>∶</a
><a name="8357"
> </a
><a name="8358" class="Symbol"
>(</a
- ><a name="8359" href="Stlc.html#636" class="InductiveConstructor"
+ ><a name="8359" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
><a name="8360"
> </a
- ><a name="8361" href="Stlc.html#609" class="InductiveConstructor Operator"
+ ><a name="8361" href="Stlc.html#2550" class="InductiveConstructor Operator"
>⇒</a
><a name="8362"
> </a
- ><a name="8363" href="Stlc.html#636" class="InductiveConstructor"
+ ><a name="8363" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
><a name="8364" class="Symbol"
>)</a
><a name="8365"
> </a
- ><a name="8366" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8366" href="Stlc.html#3520" class="InductiveConstructor Operator"
>]</a
><a name="8367"
> </a
- ><a name="8368" href="Stlc.html#727" class="InductiveConstructor"
+ ><a name="8368" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
><a name="8369"
> </a
- ><a name="8370" href="Stlc.html#917" class="Function"
+ ><a name="8370" href="Stlc.html#3875" class="Function"
>f</a
><a name="8371"
> </a
- ><a name="8372" href="Stlc.html#779" class="InductiveConstructor Operator"
+ ><a name="8372" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
><a name="8373"
> </a
- ><a name="8374" href="Stlc.html#727" class="InductiveConstructor"
+ ><a name="8374" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
><a name="8375"
> </a
- ><a name="8376" href="Stlc.html#919" class="Function"
+ ><a name="8376" href="Stlc.html#3877" class="Function"
>x</a
><a name="8377" class="Symbol"
>)</a
@@ -2538,7 +2538,7 @@ Here are proofs corresponding to the first two examples above.
>:</a
><a name="8439"
> </a
- ><a name="8440" href="Stlc.html#917" class="Function"
+ ><a name="8440" href="Stlc.html#3875" class="Function"
>f</a
><a name="8441"
> </a
@@ -2548,55 +2548,55 @@ Here are proofs corresponding to the first two examples above.
> </a
><a name="8444" class="Symbol"
>(</a
- ><a name="8445" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8445" href="Stlc.html#3520" class="InductiveConstructor Operator"
>λ[</a
><a name="8447"
> </a
- ><a name="8448" href="Stlc.html#917" class="Function"
+ ><a name="8448" href="Stlc.html#3875" class="Function"
>f</a
><a name="8449"
> </a
- ><a name="8450" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8450" href="Stlc.html#3520" class="InductiveConstructor Operator"
>∶</a
><a name="8451"
> </a
><a name="8452" class="Symbol"
>(</a
- ><a name="8453" href="Stlc.html#636" class="InductiveConstructor"
+ ><a name="8453" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
><a name="8454"
> </a
- ><a name="8455" href="Stlc.html#609" class="InductiveConstructor Operator"
+ ><a name="8455" href="Stlc.html#2550" class="InductiveConstructor Operator"
>⇒</a
><a name="8456"
> </a
- ><a name="8457" href="Stlc.html#636" class="InductiveConstructor"
+ ><a name="8457" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
><a name="8458" class="Symbol"
>)</a
><a name="8459"
> </a
- ><a name="8460" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8460" href="Stlc.html#3520" class="InductiveConstructor Operator"
>]</a
><a name="8461"
> </a
- ><a name="8462" href="Stlc.html#727" class="InductiveConstructor"
+ ><a name="8462" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
><a name="8463"
> </a
- ><a name="8464" href="Stlc.html#917" class="Function"
+ ><a name="8464" href="Stlc.html#3875" class="Function"
>f</a
><a name="8465"
> </a
- ><a name="8466" href="Stlc.html#779" class="InductiveConstructor Operator"
+ ><a name="8466" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
><a name="8467"
> </a
- ><a name="8468" href="Stlc.html#727" class="InductiveConstructor"
+ ><a name="8468" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
><a name="8469"
> </a
- ><a name="8470" href="Stlc.html#919" class="Function"
+ ><a name="8470" href="Stlc.html#3877" class="Function"
>x</a
><a name="8471" class="Symbol"
>)</a
@@ -2654,7 +2654,7 @@ Prove formally the remaining examples given above.
>:</a
><a name="8650"
> </a
- ><a name="8651" href="Stlc.html#919" class="Function"
+ ><a name="8651" href="Stlc.html#3877" class="Function"
>x</a
><a name="8652"
> </a
@@ -2664,69 +2664,69 @@ Prove formally the remaining examples given above.
> </a
><a name="8655" class="Symbol"
>((</a
- ><a name="8657" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8657" href="Stlc.html#3520" class="InductiveConstructor Operator"
>λ[</a
><a name="8659"
> </a
- ><a name="8660" href="Stlc.html#917" class="Function"
+ ><a name="8660" href="Stlc.html#3875" class="Function"
>f</a
><a name="8661"
> </a
- ><a name="8662" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8662" href="Stlc.html#3520" class="InductiveConstructor Operator"
>∶</a
><a name="8663"
> </a
><a name="8664" class="Symbol"
>(</a
- ><a name="8665" href="Stlc.html#636" class="InductiveConstructor"
+ ><a name="8665" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
><a name="8666"
> </a
- ><a name="8667" href="Stlc.html#609" class="InductiveConstructor Operator"
+ ><a name="8667" href="Stlc.html#2550" class="InductiveConstructor Operator"
>⇒</a
><a name="8668"
> </a
- ><a name="8669" href="Stlc.html#636" class="InductiveConstructor"
+ ><a name="8669" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
><a name="8670" class="Symbol"
>)</a
><a name="8671"
> </a
- ><a name="8672" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8672" href="Stlc.html#3520" class="InductiveConstructor Operator"
>]</a
><a name="8673"
> </a
- ><a name="8674" href="Stlc.html#727" class="InductiveConstructor"
+ ><a name="8674" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
><a name="8675"
> </a
- ><a name="8676" href="Stlc.html#917" class="Function"
+ ><a name="8676" href="Stlc.html#3875" class="Function"
>f</a
><a name="8677"
> </a
- ><a name="8678" href="Stlc.html#779" class="InductiveConstructor Operator"
+ ><a name="8678" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
><a name="8679"
> </a
- ><a name="8680" href="Stlc.html#727" class="InductiveConstructor"
+ ><a name="8680" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
><a name="8681"
> </a
- ><a name="8682" href="Stlc.html#919" class="Function"
+ ><a name="8682" href="Stlc.html#3877" class="Function"
>x</a
><a name="8683" class="Symbol"
>)</a
><a name="8684"
> </a
- ><a name="8685" href="Stlc.html#779" class="InductiveConstructor Operator"
+ ><a name="8685" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
><a name="8686"
> </a
- ><a name="8687" href="Stlc.html#727" class="InductiveConstructor"
+ ><a name="8687" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
><a name="8688"
> </a
- ><a name="8689" href="Stlc.html#917" class="Function"
+ ><a name="8689" href="Stlc.html#3875" class="Function"
>f</a
><a name="8690" class="Symbol"
>)</a
@@ -2741,7 +2741,7 @@ Prove formally the remaining examples given above.
>:</a
><a name="8709"
> </a
- ><a name="8710" href="Stlc.html#917" class="Function"
+ ><a name="8710" href="Stlc.html#3875" class="Function"
>f</a
><a name="8711"
> </a
@@ -2751,69 +2751,69 @@ Prove formally the remaining examples given above.
> </a
><a name="8714" class="Symbol"
>((</a
- ><a name="8716" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8716" href="Stlc.html#3520" class="InductiveConstructor Operator"
>λ[</a
><a name="8718"
> </a
- ><a name="8719" href="Stlc.html#917" class="Function"
+ ><a name="8719" href="Stlc.html#3875" class="Function"
>f</a
><a name="8720"
> </a
- ><a name="8721" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8721" href="Stlc.html#3520" class="InductiveConstructor Operator"
>∶</a
><a name="8722"
> </a
><a name="8723" class="Symbol"
>(</a
- ><a name="8724" href="Stlc.html#636" class="InductiveConstructor"
+ ><a name="8724" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
><a name="8725"
> </a
- ><a name="8726" href="Stlc.html#609" class="InductiveConstructor Operator"
+ ><a name="8726" href="Stlc.html#2550" class="InductiveConstructor Operator"
>⇒</a
><a name="8727"
> </a
- ><a name="8728" href="Stlc.html#636" class="InductiveConstructor"
+ ><a name="8728" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
><a name="8729" class="Symbol"
>)</a
><a name="8730"
> </a
- ><a name="8731" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8731" href="Stlc.html#3520" class="InductiveConstructor Operator"
>]</a
><a name="8732"
> </a
- ><a name="8733" href="Stlc.html#727" class="InductiveConstructor"
+ ><a name="8733" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
><a name="8734"
> </a
- ><a name="8735" href="Stlc.html#917" class="Function"
+ ><a name="8735" href="Stlc.html#3875" class="Function"
>f</a
><a name="8736"
> </a
- ><a name="8737" href="Stlc.html#779" class="InductiveConstructor Operator"
+ ><a name="8737" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
><a name="8738"
> </a
- ><a name="8739" href="Stlc.html#727" class="InductiveConstructor"
+ ><a name="8739" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
><a name="8740"
> </a
- ><a name="8741" href="Stlc.html#919" class="Function"
+ ><a name="8741" href="Stlc.html#3877" class="Function"
>x</a
><a name="8742" class="Symbol"
>)</a
><a name="8743"
> </a
- ><a name="8744" href="Stlc.html#779" class="InductiveConstructor Operator"
+ ><a name="8744" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
><a name="8745"
> </a
- ><a name="8746" href="Stlc.html#727" class="InductiveConstructor"
+ ><a name="8746" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
><a name="8747"
> </a
- ><a name="8748" href="Stlc.html#917" class="Function"
+ ><a name="8748" href="Stlc.html#3875" class="Function"
>f</a
><a name="8749" class="Symbol"
>)</a
@@ -2828,7 +2828,7 @@ Prove formally the remaining examples given above.
>:</a
><a name="8768"
> </a
- ><a name="8769" href="Stlc.html#919" class="Function"
+ ><a name="8769" href="Stlc.html#3877" class="Function"
>x</a
><a name="8770"
> </a
@@ -2838,75 +2838,75 @@ Prove formally the remaining examples given above.
> </a
><a name="8773" class="Symbol"
>(</a
- ><a name="8774" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8774" href="Stlc.html#3520" class="InductiveConstructor Operator"
>λ[</a
><a name="8776"
> </a
- ><a name="8777" href="Stlc.html#917" class="Function"
+ ><a name="8777" href="Stlc.html#3875" class="Function"
>f</a
><a name="8778"
> </a
- ><a name="8779" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8779" href="Stlc.html#3520" class="InductiveConstructor Operator"
>∶</a
><a name="8780"
> </a
><a name="8781" class="Symbol"
>(</a
- ><a name="8782" href="Stlc.html#636" class="InductiveConstructor"
+ ><a name="8782" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
><a name="8783"
> </a
- ><a name="8784" href="Stlc.html#609" class="InductiveConstructor Operator"
+ ><a name="8784" href="Stlc.html#2550" class="InductiveConstructor Operator"
>⇒</a
><a name="8785"
> </a
- ><a name="8786" href="Stlc.html#636" class="InductiveConstructor"
+ ><a name="8786" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
><a name="8787" class="Symbol"
>)</a
><a name="8788"
> </a
- ><a name="8789" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8789" href="Stlc.html#3520" class="InductiveConstructor Operator"
>]</a
><a name="8790"
> </a
- ><a name="8791" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8791" href="Stlc.html#3520" class="InductiveConstructor Operator"
>λ[</a
><a name="8793"
> </a
- ><a name="8794" href="Stlc.html#919" class="Function"
+ ><a name="8794" href="Stlc.html#3877" class="Function"
>x</a
><a name="8795"
> </a
- ><a name="8796" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8796" href="Stlc.html#3520" class="InductiveConstructor Operator"
>∶</a
><a name="8797"
> </a
- ><a name="8798" href="Stlc.html#636" class="InductiveConstructor"
+ ><a name="8798" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
><a name="8799"
> </a
- ><a name="8800" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8800" href="Stlc.html#3520" class="InductiveConstructor Operator"
>]</a
><a name="8801"
> </a
- ><a name="8802" href="Stlc.html#727" class="InductiveConstructor"
+ ><a name="8802" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
><a name="8803"
> </a
- ><a name="8804" href="Stlc.html#917" class="Function"
+ ><a name="8804" href="Stlc.html#3875" class="Function"
>f</a
><a name="8805"
> </a
- ><a name="8806" href="Stlc.html#779" class="InductiveConstructor Operator"
+ ><a name="8806" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
><a name="8807"
> </a
- ><a name="8808" href="Stlc.html#727" class="InductiveConstructor"
+ ><a name="8808" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
><a name="8809"
> </a
- ><a name="8810" href="Stlc.html#919" class="Function"
+ ><a name="8810" href="Stlc.html#3877" class="Function"
>x</a
><a name="8811" class="Symbol"
>)</a
@@ -2921,7 +2921,7 @@ Prove formally the remaining examples given above.
>:</a
><a name="8830"
> </a
- ><a name="8831" href="Stlc.html#917" class="Function"
+ ><a name="8831" href="Stlc.html#3875" class="Function"
>f</a
><a name="8832"
> </a
@@ -2931,75 +2931,75 @@ Prove formally the remaining examples given above.
> </a
><a name="8835" class="Symbol"
>(</a
- ><a name="8836" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8836" href="Stlc.html#3520" class="InductiveConstructor Operator"
>λ[</a
><a name="8838"
> </a
- ><a name="8839" href="Stlc.html#917" class="Function"
+ ><a name="8839" href="Stlc.html#3875" class="Function"
>f</a
><a name="8840"
> </a
- ><a name="8841" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8841" href="Stlc.html#3520" class="InductiveConstructor Operator"
>∶</a
><a name="8842"
> </a
><a name="8843" class="Symbol"
>(</a
- ><a name="8844" href="Stlc.html#636" class="InductiveConstructor"
+ ><a name="8844" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
><a name="8845"
> </a
- ><a name="8846" href="Stlc.html#609" class="InductiveConstructor Operator"
+ ><a name="8846" href="Stlc.html#2550" class="InductiveConstructor Operator"
>⇒</a
><a name="8847"
> </a
- ><a name="8848" href="Stlc.html#636" class="InductiveConstructor"
+ ><a name="8848" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
><a name="8849" class="Symbol"
>)</a
><a name="8850"
> </a
- ><a name="8851" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8851" href="Stlc.html#3520" class="InductiveConstructor Operator"
>]</a
><a name="8852"
> </a
- ><a name="8853" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8853" href="Stlc.html#3520" class="InductiveConstructor Operator"
>λ[</a
><a name="8855"
> </a
- ><a name="8856" href="Stlc.html#919" class="Function"
+ ><a name="8856" href="Stlc.html#3877" class="Function"
>x</a
><a name="8857"
> </a
- ><a name="8858" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8858" href="Stlc.html#3520" class="InductiveConstructor Operator"
>∶</a
><a name="8859"
> </a
- ><a name="8860" href="Stlc.html#636" class="InductiveConstructor"
+ ><a name="8860" href="Stlc.html#2577" class="InductiveConstructor"
>𝔹</a
><a name="8861"
> </a
- ><a name="8862" href="Stlc.html#743" class="InductiveConstructor Operator"
+ ><a name="8862" href="Stlc.html#3520" class="InductiveConstructor Operator"
>]</a
><a name="8863"
> </a
- ><a name="8864" href="Stlc.html#727" class="InductiveConstructor"
+ ><a name="8864" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
><a name="8865"
> </a
- ><a name="8866" href="Stlc.html#917" class="Function"
+ ><a name="8866" href="Stlc.html#3875" class="Function"
>f</a
><a name="8867"
> </a
- ><a name="8868" href="Stlc.html#779" class="InductiveConstructor Operator"
+ ><a name="8868" href="Stlc.html#3556" class="InductiveConstructor Operator"
>·</a
><a name="8869"
> </a
- ><a name="8870" href="Stlc.html#727" class="InductiveConstructor"
+ ><a name="8870" href="Stlc.html#3504" class="InductiveConstructor"
>`</a
><a name="8871"
> </a
- ><a name="8872" href="Stlc.html#919" class="Function"
+ ><a name="8872" href="Stlc.html#3877" class="Function"
>x</a
><a name="8873" class="Symbol"
>)</a
@@ -3076,7 +3076,7 @@ then `Γ` must assign a type to `x`.
>Γ</a
><a name="9392"
> </a
- ><a name="9393" href="Stlc.html#3112" class="Datatype Operator"
+ ><a name="9393" href="Stlc.html#6070" class="Datatype Operator"
>⊢</a
><a name="9394"
> </a
@@ -3084,7 +3084,7 @@ then `Γ` must assign a type to `x`.
>M</a
><a name="9396"
> </a
- ><a name="9397" href="Stlc.html#3112" class="Datatype Operator"
+ ><a name="9397" href="Stlc.html#6070" class="Datatype Operator"
>∶</a
><a name="9398"
> </a
@@ -3138,7 +3138,7 @@ _Proof_: We show, by induction on the proof that `x` appears
free in `M`, that, for all contexts `Γ`, if `M` is well
typed under `Γ`, then `Γ` assigns some type to `x`.
- - If the last rule used was `free-\``, then `M = \` x`, and from
+ - If the last rule used was `` free-` ``, then `M = `` `x ``, and from
the assumption that `M` is well typed under `Γ` we have
immediately that `Γ` assigns a type to `x`.
@@ -3164,454 +3164,454 @@ _Proof_: We show, by induction on the proof that `x` appears
<pre class="Agda">
-<a name="10865" href="StlcProp.html#9356" class="Function"
+<a name="10871" href="StlcProp.html#9356" class="Function"
>free-lemma</a
- ><a name="10875"
+ ><a name="10881"
> </a
- ><a name="10876" href="StlcProp.html#7689" class="InductiveConstructor"
+ ><a name="10882" href="StlcProp.html#7689" class="InductiveConstructor"
>free-`</a
- ><a name="10882"
+ ><a name="10888"
> </a
- ><a name="10883" class="Symbol"
+ ><a name="10889" class="Symbol"
>(</a
- ><a name="10884" href="Stlc.html#3156" class="InductiveConstructor"
+ ><a name="10890" href="Stlc.html#6114" class="InductiveConstructor"
>Ax</a
- ><a name="10886"
- > </a
- ><a name="10887" href="StlcProp.html#10887" class="Bound"
- >Γx≡A</a
- ><a name="10891" class="Symbol"
- >)</a
><a name="10892"
> </a
- ><a name="10893" class="Symbol"
- >=</a
- ><a name="10894"
- > </a
- ><a name="10895" class="Symbol"
- >(_</a
- ><a name="10897"
- > </a
- ><a name="10898" href="https://agda.github.io/agda-stdlib/Data.Product.html#509" class="InductiveConstructor Operator"
- >,</a
- ><a name="10899"
- > </a
- ><a name="10900" href="StlcProp.html#10887" class="Bound"
+ ><a name="10893" href="StlcProp.html#10893" class="Bound"
>Γx≡A</a
- ><a name="10904" class="Symbol"
+ ><a name="10897" class="Symbol"
>)</a
+ ><a name="10898"
+ > </a
+ ><a name="10899" class="Symbol"
+ >=</a
+ ><a name="10900"
+ > </a
+ ><a name="10901" class="Symbol"
+ >(_</a
+ ><a name="10903"
+ > </a
+ ><a name="10904" href="https://agda.github.io/agda-stdlib/Data.Product.html#509" class="InductiveConstructor Operator"
+ >,</a
><a name="10905"
+ > </a
+ ><a name="10906" href="StlcProp.html#10893" class="Bound"
+ >Γx≡A</a
+ ><a name="10910" class="Symbol"
+ >)</a
+ ><a name="10911"
>
</a
- ><a name="10906" href="StlcProp.html#9356" class="Function"
+ ><a name="10912" href="StlcProp.html#9356" class="Function"
>free-lemma</a
- ><a name="10916"
+ ><a name="10922"
> </a
- ><a name="10917" class="Symbol"
+ ><a name="10923" class="Symbol"
>(</a
- ><a name="10918" href="StlcProp.html#7778" class="InductiveConstructor"
+ ><a name="10924" href="StlcProp.html#7778" class="InductiveConstructor"
>free-·₁</a
- ><a name="10925"
+ ><a name="10931"
> </a
- ><a name="10926" href="StlcProp.html#10926" class="Bound"
+ ><a name="10932" href="StlcProp.html#10932" class="Bound"
>x∈L</a
- ><a name="10929" class="Symbol"
+ ><a name="10935" class="Symbol"
>)</a
- ><a name="10930"
+ ><a name="10936"
> </a
- ><a name="10931" class="Symbol"
+ ><a name="10937" class="Symbol"
>(</a
- ><a name="10932" href="Stlc.html#3287" class="InductiveConstructor"
+ ><a name="10938" href="Stlc.html#6245" class="InductiveConstructor"
>⇒-E</a
- ><a name="10935"
+ ><a name="10941"
> </a
- ><a name="10936" href="StlcProp.html#10936" class="Bound"
+ ><a name="10942" href="StlcProp.html#10942" class="Bound"
>⊢L</a
- ><a name="10938"
- > </a
- ><a name="10939" href="StlcProp.html#10939" class="Bound"
- >⊢M</a
- ><a name="10941" class="Symbol"
- >)</a
- ><a name="10942"
- > </a
- ><a name="10943" class="Symbol"
- >=</a
><a name="10944"
> </a
- ><a name="10945" href="StlcProp.html#9356" class="Function"
+ ><a name="10945" href="StlcProp.html#10945" class="Bound"
+ >⊢M</a
+ ><a name="10947" class="Symbol"
+ >)</a
+ ><a name="10948"
+ > </a
+ ><a name="10949" class="Symbol"
+ >=</a
+ ><a name="10950"
+ > </a
+ ><a name="10951" href="StlcProp.html#9356" class="Function"
>free-lemma</a
- ><a name="10955"
+ ><a name="10961"
> </a
- ><a name="10956" href="StlcProp.html#10926" class="Bound"
+ ><a name="10962" href="StlcProp.html#10932" class="Bound"
>x∈L</a
- ><a name="10959"
+ ><a name="10965"
> </a
- ><a name="10960" href="StlcProp.html#10936" class="Bound"
+ ><a name="10966" href="StlcProp.html#10942" class="Bound"
>⊢L</a
- ><a name="10962"
+ ><a name="10968"
>
</a
- ><a name="10963" href="StlcProp.html#9356" class="Function"
+ ><a name="10969" href="StlcProp.html#9356" class="Function"
>free-lemma</a
- ><a name="10973"
+ ><a name="10979"
> </a
- ><a name="10974" class="Symbol"
+ ><a name="10980" class="Symbol"
>(</a
- ><a name="10975" href="StlcProp.html#7822" class="InductiveConstructor"
+ ><a name="10981" href="StlcProp.html#7822" class="InductiveConstructor"
>free-·₂</a
- ><a name="10982"
+ ><a name="10988"
> </a
- ><a name="10983" href="StlcProp.html#10983" class="Bound"
+ ><a name="10989" href="StlcProp.html#10989" class="Bound"
>x∈M</a
- ><a name="10986" class="Symbol"
+ ><a name="10992" class="Symbol"
>)</a
- ><a name="10987"
+ ><a name="10993"
> </a
- ><a name="10988" class="Symbol"
+ ><a name="10994" class="Symbol"
>(</a
- ><a name="10989" href="Stlc.html#3287" class="InductiveConstructor"
+ ><a name="10995" href="Stlc.html#6245" class="InductiveConstructor"
>⇒-E</a
- ><a name="10992"
+ ><a name="10998"
> </a
- ><a name="10993" href="StlcProp.html#10993" class="Bound"
+ ><a name="10999" href="StlcProp.html#10999" class="Bound"
>⊢L</a
- ><a name="10995"
- > </a
- ><a name="10996" href="StlcProp.html#10996" class="Bound"
- >⊢M</a
- ><a name="10998" class="Symbol"
- >)</a
- ><a name="10999"
- > </a
- ><a name="11000" class="Symbol"
- >=</a
><a name="11001"
> </a
- ><a name="11002" href="StlcProp.html#9356" class="Function"
- >free-lemma</a
- ><a name="11012"
- > </a
- ><a name="11013" href="StlcProp.html#10983" class="Bound"
- >x∈M</a
- ><a name="11016"
- > </a
- ><a name="11017" href="StlcProp.html#10996" class="Bound"
+ ><a name="11002" href="StlcProp.html#11002" class="Bound"
>⊢M</a
- ><a name="11019"
+ ><a name="11004" class="Symbol"
+ >)</a
+ ><a name="11005"
+ > </a
+ ><a name="11006" class="Symbol"
+ >=</a
+ ><a name="11007"
+ > </a
+ ><a name="11008" href="StlcProp.html#9356" class="Function"
+ >free-lemma</a
+ ><a name="11018"
+ > </a
+ ><a name="11019" href="StlcProp.html#10989" class="Bound"
+ >x∈M</a
+ ><a name="11022"
+ > </a
+ ><a name="11023" href="StlcProp.html#11002" class="Bound"
+ >⊢M</a
+ ><a name="11025"
>
</a
- ><a name="11020" href="StlcProp.html#9356" class="Function"
+ ><a name="11026" href="StlcProp.html#9356" class="Function"
>free-lemma</a
- ><a name="11030"
+ ><a name="11036"
> </a
- ><a name="11031" class="Symbol"
+ ><a name="11037" class="Symbol"
>(</a
- ><a name="11032" href="StlcProp.html#7866" class="InductiveConstructor"
+ ><a name="11038" href="StlcProp.html#7866" class="InductiveConstructor"
>free-if₁</a
- ><a name="11040"
+ ><a name="11046"
> </a
- ><a name="11041" href="StlcProp.html#11041" class="Bound"
+ ><a name="11047" href="StlcProp.html#11047" class="Bound"
>x∈L</a
- ><a name="11044" class="Symbol"
+ ><a name="11050" class="Symbol"
>)</a
- ><a name="11045"
+ ><a name="11051"
> </a
- ><a name="11046" class="Symbol"
+ ><a name="11052" class="Symbol"
>(</a
- ><a name="11047" href="Stlc.html#3434" class="InductiveConstructor"
+ ><a name="11053" href="Stlc.html#6392" class="InductiveConstructor"
>𝔹-E</a
- ><a name="11050"
- > </a
- ><a name="11051" href="StlcProp.html#11051" class="Bound"
- >⊢L</a
- ><a name="11053"
- > </a
- ><a name="11054" href="StlcProp.html#11054" class="Bound"
- >⊢M</a
><a name="11056"
> </a
><a name="11057" href="StlcProp.html#11057" class="Bound"
- >⊢N</a
- ><a name="11059" class="Symbol"
- >)</a
- ><a name="11060"
+ >⊢L</a
+ ><a name="11059"
> </a
- ><a name="11061" class="Symbol"
- >=</a
+ ><a name="11060" href="StlcProp.html#11060" class="Bound"
+ >⊢M</a
><a name="11062"
> </a
- ><a name="11063" href="StlcProp.html#9356" class="Function"
+ ><a name="11063" href="StlcProp.html#11063" class="Bound"
+ >⊢N</a
+ ><a name="11065" class="Symbol"
+ >)</a
+ ><a name="11066"
+ > </a
+ ><a name="11067" class="Symbol"
+ >=</a
+ ><a name="11068"
+ > </a
+ ><a name="11069" href="StlcProp.html#9356" class="Function"
>free-lemma</a
- ><a name="11073"
+ ><a name="11079"
> </a
- ><a name="11074" href="StlcProp.html#11041" class="Bound"
+ ><a name="11080" href="StlcProp.html#11047" class="Bound"
>x∈L</a
- ><a name="11077"
+ ><a name="11083"
> </a
- ><a name="11078" href="StlcProp.html#11051" class="Bound"
+ ><a name="11084" href="StlcProp.html#11057" class="Bound"
>⊢L</a
- ><a name="11080"
+ ><a name="11086"
>
</a
- ><a name="11081" href="StlcProp.html#9356" class="Function"
+ ><a name="11087" href="StlcProp.html#9356" class="Function"
>free-lemma</a
- ><a name="11091"
+ ><a name="11097"
> </a
- ><a name="11092" class="Symbol"
+ ><a name="11098" class="Symbol"
>(</a
- ><a name="11093" href="StlcProp.html#7926" class="InductiveConstructor"
+ ><a name="11099" href="StlcProp.html#7926" class="InductiveConstructor"
>free-if₂</a
- ><a name="11101"
+ ><a name="11107"
> </a
- ><a name="11102" href="StlcProp.html#11102" class="Bound"
+ ><a name="11108" href="StlcProp.html#11108" class="Bound"
>x∈M</a
- ><a name="11105" class="Symbol"
+ ><a name="11111" class="Symbol"
>)</a
- ><a name="11106"
+ ><a name="11112"
> </a
- ><a name="11107" class="Symbol"
+ ><a name="11113" class="Symbol"
>(</a
- ><a name="11108" href="Stlc.html#3434" class="InductiveConstructor"
+ ><a name="11114" href="Stlc.html#6392" class="InductiveConstructor"
>𝔹-E</a
- ><a name="11111"
- > </a
- ><a name="11112" href="StlcProp.html#11112" class="Bound"
- >⊢L</a
- ><a name="11114"
- > </a
- ><a name="11115" href="StlcProp.html#11115" class="Bound"
- >⊢M</a
><a name="11117"
> </a
><a name="11118" href="StlcProp.html#11118" class="Bound"
- >⊢N</a
- ><a name="11120" class="Symbol"
- >)</a
- ><a name="11121"
+ >⊢L</a
+ ><a name="11120"
> </a
- ><a name="11122" class="Symbol"
- >=</a
+ ><a name="11121" href="StlcProp.html#11121" class="Bound"
+ >⊢M</a
><a name="11123"
> </a
- ><a name="11124" href="StlcProp.html#9356" class="Function"
+ ><a name="11124" href="StlcProp.html#11124" class="Bound"
+ >⊢N</a
+ ><a name="11126" class="Symbol"
+ >)</a
+ ><a name="11127"
+ > </a
+ ><a name="11128" class="Symbol"
+ >=</a
+ ><a name="11129"
+ > </a
+ ><a name="11130" href="StlcProp.html#9356" class="Function"
>free-lemma</a
- ><a name="11134"
+ ><a name="11140"
> </a
- ><a name="11135" href="StlcProp.html#11102" class="Bound"
+ ><a name="11141" href="StlcProp.html#11108" class="Bound"
>x∈M</a
- ><a name="11138"
+ ><a name="11144"
> </a
- ><a name="11139" href="StlcProp.html#11115" class="Bound"
+ ><a name="11145" href="StlcProp.html#11121" class="Bound"
>⊢M</a
- ><a name="11141"
+ ><a name="11147"
>
</a
- ><a name="11142" href="StlcProp.html#9356" class="Function"
+ ><a name="11148" href="StlcProp.html#9356" class="Function"
>free-lemma</a
- ><a name="11152"
+ ><a name="11158"
> </a
- ><a name="11153" class="Symbol"
+ ><a name="11159" class="Symbol"
>(</a
- ><a name="11154" href="StlcProp.html#7986" class="InductiveConstructor"
+ ><a name="11160" href="StlcProp.html#7986" class="InductiveConstructor"
>free-if₃</a
- ><a name="11162"
+ ><a name="11168"
> </a
- ><a name="11163" href="StlcProp.html#11163" class="Bound"
+ ><a name="11169" href="StlcProp.html#11169" class="Bound"
>x∈N</a
- ><a name="11166" class="Symbol"
+ ><a name="11172" class="Symbol"
>)</a
- ><a name="11167"
+ ><a name="11173"
> </a
- ><a name="11168" class="Symbol"
+ ><a name="11174" class="Symbol"
>(</a
- ><a name="11169" href="Stlc.html#3434" class="InductiveConstructor"
+ ><a name="11175" href="Stlc.html#6392" class="InductiveConstructor"
>𝔹-E</a
- ><a name="11172"
- > </a
- ><a name="11173" href="StlcProp.html#11173" class="Bound"
- >⊢L</a
- ><a name="11175"
- > </a
- ><a name="11176" href="StlcProp.html#11176" class="Bound"
- >⊢M</a
><a name="11178"
> </a
><a name="11179" href="StlcProp.html#11179" class="Bound"
- >⊢N</a
- ><a name="11181" class="Symbol"
- >)</a
- ><a name="11182"
+ >⊢L</a
+ ><a name="11181"
> </a
- ><a name="11183" class="Symbol"
- >=</a
+ ><a name="11182" href="StlcProp.html#11182" class="Bound"
+ >⊢M</a
><a name="11184"
> </a
- ><a name="11185" href="StlcProp.html#9356" class="Function"
- >free-lemma</a
- ><a name="11195"
- > </a
- ><a name="11196" href="StlcProp.html#11163" class="Bound"
- >x∈N</a
- ><a name="11199"
- > </a
- ><a name="11200" href="StlcProp.html#11179" class="Bound"
+ ><a name="11185" href="StlcProp.html#11185" class="Bound"
>⊢N</a
- ><a name="11202"
+ ><a name="11187" class="Symbol"
+ >)</a
+ ><a name="11188"
+ > </a
+ ><a name="11189" class="Symbol"
+ >=</a
+ ><a name="11190"
+ > </a
+ ><a name="11191" href="StlcProp.html#9356" class="Function"
+ >free-lemma</a
+ ><a name="11201"
+ > </a
+ ><a name="11202" href="StlcProp.html#11169" class="Bound"
+ >x∈N</a
+ ><a name="11205"
+ > </a
+ ><a name="11206" href="StlcProp.html#11185" class="Bound"
+ >⊢N</a
+ ><a name="11208"
>
</a
- ><a name="11203" href="StlcProp.html#9356" class="Function"
+ ><a name="11209" href="StlcProp.html#9356" class="Function"
>free-lemma</a
- ><a name="11213"
+ ><a name="11219"
> </a
- ><a name="11214" class="Symbol"
+ ><a name="11220" class="Symbol"
>(</a
- ><a name="11215" href="StlcProp.html#7717" class="InductiveConstructor"
+ ><a name="11221" href="StlcProp.html#7717" class="InductiveConstructor"
>free-λ</a
- ><a name="11221"
+ ><a name="11227"
> </a
- ><a name="11222" class="Symbol"
- >{</a
- ><a name="11223" href="StlcProp.html#11223" class="Bound"
- >x</a
- ><a name="11224" class="Symbol"
- >}</a
- ><a name="11225"
- > </a
- ><a name="11226" class="Symbol"
- >{</a
- ><a name="11227" href="StlcProp.html#11227" class="Bound"
- >y</a
><a name="11228" class="Symbol"
- >}</a
- ><a name="11229"
- > </a
- ><a name="11230" href="StlcProp.html#11230" class="Bound"
- >y≢x</a
- ><a name="11233"
- > </a
- ><a name="11234" href="StlcProp.html#11234" class="Bound"
- >x∈N</a
- ><a name="11237" class="Symbol"
- >)</a
- ><a name="11238"
- > </a
- ><a name="11239" class="Symbol"
- >(</a
- ><a name="11240" href="Stlc.html#3210" class="InductiveConstructor"
- >⇒-I</a
- ><a name="11243"
- > </a
- ><a name="11244" href="StlcProp.html#11244" class="Bound"
- >⊢N</a
- ><a name="11246" class="Symbol"
- >)</a
- ><a name="11247"
- > </a
- ><a name="11248" class="Keyword"
- >with</a
- ><a name="11252"
- > </a
- ><a name="11253" href="StlcProp.html#9356" class="Function"
- >free-lemma</a
- ><a name="11263"
- > </a
- ><a name="11264" href="StlcProp.html#11234" class="Bound"
- >x∈N</a
- ><a name="11267"
- > </a
- ><a name="11268" href="StlcProp.html#11244" class="Bound"
- >⊢N</a
- ><a name="11270"
- >
-</a
- ><a name="11271" class="Symbol"
- >...</a
- ><a name="11274"
- > </a
- ><a name="11275" class="Symbol"
- >|</a
- ><a name="11276"
- > </a
- ><a name="11277" href="StlcProp.html#11277" class="Bound"
- >Γx≡C</a
- ><a name="11281"
- > </a
- ><a name="11282" class="Keyword"
- >with</a
- ><a name="11286"
- > </a
- ><a name="11287" href="StlcProp.html#11227" class="Bound"
- >y</a
- ><a name="11288"
- > </a
- ><a name="11289" href="Maps.html#2509" class="Function Operator"
- >≟</a
- ><a name="11290"
- > </a
- ><a name="11291" href="StlcProp.html#11223" class="Bound"
+ >{</a
+ ><a name="11229" href="StlcProp.html#11229" class="Bound"
>x</a
- ><a name="11292"
+ ><a name="11230" class="Symbol"
+ >}</a
+ ><a name="11231"
+ > </a
+ ><a name="11232" class="Symbol"
+ >{</a
+ ><a name="11233" href="StlcProp.html#11233" class="Bound"
+ >y</a
+ ><a name="11234" class="Symbol"
+ >}</a
+ ><a name="11235"
+ > </a
+ ><a name="11236" href="StlcProp.html#11236" class="Bound"
+ >y≢x</a
+ ><a name="11239"
+ > </a
+ ><a name="11240" href="StlcProp.html#11240" class="Bound"
+ >x∈N</a
+ ><a name="11243" class="Symbol"
+ >)</a
+ ><a name="11244"
+ > </a
+ ><a name="11245" class="Symbol"
+ >(</a
+ ><a name="11246" href="Stlc.html#6168" class="InductiveConstructor"
+ >⇒-I</a
+ ><a name="11249"
+ > </a
+ ><a name="11250" href="StlcProp.html#11250" class="Bound"
+ >⊢N</a
+ ><a name="11252" class="Symbol"
+ >)</a
+ ><a name="11253"
+ > </a
+ ><a name="11254" class="Keyword"
+ >with</a
+ ><a name="11258"
+ > </a
+ ><a name="11259" href="StlcProp.html#9356" class="Function"
+ >free-lemma</a
+ ><a name="11269"
+ > </a
+ ><a name="11270" href="StlcProp.html#11240" class="Bound"
+ >x∈N</a
+ ><a name="11273"
+ > </a
+ ><a name="11274" href="StlcProp.html#11250" class="Bound"
+ >⊢N</a
+ ><a name="11276"
>
</a
- ><a name="11293" class="Symbol"
+ ><a name="11277" class="Symbol"
>...</a
+ ><a name="11280"
+ > </a
+ ><a name="11281" class="Symbol"
+ >|</a
+ ><a name="11282"
+ > </a
+ ><a name="11283" href="StlcProp.html#11283" class="Bound"
+ >Γx≡C</a
+ ><a name="11287"
+ > </a
+ ><a name="11288" class="Keyword"
+ >with</a
+ ><a name="11292"
+ > </a
+ ><a name="11293" href="StlcProp.html#11233" class="Bound"
+ >y</a
+ ><a name="11294"
+ > </a
+ ><a name="11295" href="Maps.html#2509" class="Function Operator"
+ >≟</a
><a name="11296"
> </a
- ><a name="11297" class="Symbol"
- >|</a
+ ><a name="11297" href="StlcProp.html#11229" class="Bound"
+ >x</a
><a name="11298"
- > </a
- ><a name="11299" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#520" class="InductiveConstructor"
- >yes</a
- ><a name="11302"
- > </a
- ><a name="11303" href="StlcProp.html#11303" class="Bound"
- >y≡x</a
- ><a name="11306"
- > </a
- ><a name="11307" class="Symbol"
- >=</a
- ><a name="11308"
- > </a
- ><a name="11309" href="https://agda.github.io/agda-stdlib/Data.Empty.html#348" class="Function"
- >⊥-elim</a
- ><a name="11315"
- > </a
- ><a name="11316" class="Symbol"
- >(</a
- ><a name="11317" href="StlcProp.html#11230" class="Bound"
- >y≢x</a
- ><a name="11320"
- > </a
- ><a name="11321" href="StlcProp.html#11303" class="Bound"
- >y≡x</a
- ><a name="11324" class="Symbol"
- >)</a
- ><a name="11325"
>
</a
- ><a name="11326" class="Symbol"
+ ><a name="11299" class="Symbol"
>...</a
- ><a name="11329"
+ ><a name="11302"
> </a
- ><a name="11330" class="Symbol"
+ ><a name="11303" class="Symbol"
>|</a
- ><a name="11331"
+ ><a name="11304"
> </a
- ><a name="11332" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#547" class="InductiveConstructor"
- >no</a
- ><a name="11334"
- > </a
- ><a name="11336" class="Symbol"
- >_</a
- ><a name="11337"
- > </a
- ><a name="11340" class="Symbol"
+ ><a name="11305" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#520" class="InductiveConstructor"
+ >yes</a
+ ><a name="11308"
+ > </a
+ ><a name="11309" href="StlcProp.html#11309" class="Bound"
+ >y≡x</a
+ ><a name="11312"
+ > </a
+ ><a name="11313" class="Symbol"
>=</a
- ><a name="11341"
+ ><a name="11314"
> </a
- ><a name="11342" href="StlcProp.html#11277" class="Bound"
+ ><a name="11315" href="https://agda.github.io/agda-stdlib/Data.Empty.html#348" class="Function"
+ >⊥-elim</a
+ ><a name="11321"
+ > </a
+ ><a name="11322" class="Symbol"
+ >(</a
+ ><a name="11323" href="StlcProp.html#11236" class="Bound"
+ >y≢x</a
+ ><a name="11326"
+ > </a
+ ><a name="11327" href="StlcProp.html#11309" class="Bound"
+ >y≡x</a
+ ><a name="11330" class="Symbol"
+ >)</a
+ ><a name="11331"
+ >
+</a
+ ><a name="11332" class="Symbol"
+ >...</a
+ ><a name="11335"
+ > </a
+ ><a name="11336" class="Symbol"
+ >|</a
+ ><a name="11337"
+ > </a
+ ><a name="11338" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#547" class="InductiveConstructor"
+ >no</a
+ ><a name="11340"
+ > </a
+ ><a name="11342" class="Symbol"
+ >_</a
+ ><a name="11343"
+ > </a
+ ><a name="11346" class="Symbol"
+ >=</a
+ ><a name="11347"
+ > </a
+ ><a name="11348" href="StlcProp.html#11283" class="Bound"
>Γx≡C</a
>
@@ -3629,68 +3629,68 @@ typed in the empty context is closed (has no free variables).
<pre class="Agda">
-<a name="11779" class="Keyword"
+<a name="11785" class="Keyword"
>postulate</a
- ><a name="11788"
+ ><a name="11794"
>
</a
- ><a name="11791" href="StlcProp.html#11791" class="Postulate"
+ ><a name="11797" href="StlcProp.html#11797" class="Postulate"
>∅⊢-closed</a
- ><a name="11800"
+ ><a name="11806"
> </a
- ><a name="11801" class="Symbol"
+ ><a name="11807" class="Symbol"
>:</a
- ><a name="11802"
+ ><a name="11808"
> </a
- ><a name="11803" class="Symbol"
- >∀</a
- ><a name="11804"
- > </a
- ><a name="11805" class="Symbol"
- >{</a
- ><a name="11806" href="StlcProp.html#11806" class="Bound"
- >M</a
- ><a name="11807"
- > </a
- ><a name="11808" href="StlcProp.html#11808" class="Bound"
- >A</a
><a name="11809" class="Symbol"
- >}</a
+ >∀</a
><a name="11810"
> </a
><a name="11811" class="Symbol"
- >→</a
- ><a name="11812"
+ >{</a
+ ><a name="11812" href="StlcProp.html#11812" class="Bound"
+ >M</a
+ ><a name="11813"
> </a
- ><a name="11813" href="Maps.html#10265" class="Function"
- >∅</a
- ><a name="11814"
- > </a
- ><a name="11815" href="Stlc.html#3112" class="Datatype Operator"
- >⊢</a
+ ><a name="11814" href="StlcProp.html#11814" class="Bound"
+ >A</a
+ ><a name="11815" class="Symbol"
+ >}</a
><a name="11816"
> </a
- ><a name="11817" href="StlcProp.html#11806" class="Bound"
- >M</a
+ ><a name="11817" class="Symbol"
+ >→</a
><a name="11818"
> </a
- ><a name="11819" href="Stlc.html#3112" class="Datatype Operator"
- >∶</a
+ ><a name="11819" href="Maps.html#10265" class="Function"
+ >∅</a
><a name="11820"
> </a
- ><a name="11821" href="StlcProp.html#11808" class="Bound"
- >A</a
+ ><a name="11821" href="Stlc.html#6070" class="Datatype Operator"
+ >⊢</a
><a name="11822"
> </a
- ><a name="11823" class="Symbol"
- >→</a
+ ><a name="11823" href="StlcProp.html#11812" class="Bound"
+ >M</a
><a name="11824"
> </a
- ><a name="11825" href="StlcProp.html#8176" class="Function"
- >closed</a
- ><a name="11831"
+ ><a name="11825" href="Stlc.html#6070" class="Datatype Operator"
+ >∶</a
+ ><a name="11826"
> </a
- ><a name="11832" href="StlcProp.html#11806" class="Bound"
+ ><a name="11827" href="StlcProp.html#11814" class="Bound"
+ >A</a
+ ><a name="11828"
+ > </a
+ ><a name="11829" class="Symbol"
+ >→</a
+ ><a name="11830"
+ > </a
+ ><a name="11831" href="StlcProp.html#8176" class="Function"
+ >closed</a
+ ><a name="11837"
+ > </a
+ ><a name="11838" href="StlcProp.html#11812" class="Bound"
>M</a
>
@@ -3699,294 +3699,294 @@ typed in the empty context is closed (has no free variables).
<div class="hidden">
<pre class="Agda">
-<a name="11880" href="StlcProp.html#11880" class="Function"
+<a name="11886" href="StlcProp.html#11886" class="Function"
>contradiction</a
- ><a name="11893"
+ ><a name="11899"
> </a
- ><a name="11894" class="Symbol"
+ ><a name="11900" class="Symbol"
>:</a
- ><a name="11895"
+ ><a name="11901"
> </a
- ><a name="11896" class="Symbol"
+ ><a name="11902" class="Symbol"
>∀</a
- ><a name="11897"
+ ><a name="11903"
> </a
- ><a name="11898" class="Symbol"
+ ><a name="11904" class="Symbol"
>{</a
- ><a name="11899" href="StlcProp.html#11899" class="Bound"
+ ><a name="11905" href="StlcProp.html#11905" class="Bound"
>X</a
- ><a name="11900"
+ ><a name="11906"
> </a
- ><a name="11901" class="Symbol"
+ ><a name="11907" class="Symbol"
>:</a
- ><a name="11902"
+ ><a name="11908"
> </a
- ><a name="11903" class="PrimitiveType"
+ ><a name="11909" class="PrimitiveType"
>Set</a
- ><a name="11906" class="Symbol"
- >}</a
- ><a name="11907"
- > </a
- ><a name="11908" class="Symbol"
- >→</a
- ><a name="11909"
- > </a
- ><a name="11910" class="Symbol"
- >∀</a
- ><a name="11911"
- > </a
><a name="11912" class="Symbol"
- >{</a
- ><a name="11913" href="StlcProp.html#11913" class="Bound"
- >x</a
- ><a name="11914"
- > </a
- ><a name="11915" class="Symbol"
- >:</a
- ><a name="11916"
- > </a
- ><a name="11917" href="StlcProp.html#11899" class="Bound"
- >X</a
- ><a name="11918" class="Symbol"
>}</a
- ><a name="11919"
+ ><a name="11913"
> </a
- ><a name="11920" class="Symbol"
+ ><a name="11914" class="Symbol"
>→</a
- ><a name="11921"
+ ><a name="11915"
> </a
- ><a name="11922" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#414" class="Function Operator"
- >¬</a
- ><a name="11923"
+ ><a name="11916" class="Symbol"
+ >∀</a
+ ><a name="11917"
> </a
- ><a name="11924" class="Symbol"
- >(</a
- ><a name="11925" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#83" class="Datatype Operator"
- >_≡_</a
- ><a name="11928"
- > </a
- ><a name="11929" class="Symbol"
+ ><a name="11918" class="Symbol"
>{</a
- ><a name="11930" class="Argument"
+ ><a name="11919" href="StlcProp.html#11919" class="Bound"
+ >x</a
+ ><a name="11920"
+ > </a
+ ><a name="11921" class="Symbol"
+ >:</a
+ ><a name="11922"
+ > </a
+ ><a name="11923" href="StlcProp.html#11905" class="Bound"
+ >X</a
+ ><a name="11924" class="Symbol"
+ >}</a
+ ><a name="11925"
+ > </a
+ ><a name="11926" class="Symbol"
+ >→</a
+ ><a name="11927"
+ > </a
+ ><a name="11928" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#414" class="Function Operator"
+ >¬</a
+ ><a name="11929"
+ > </a
+ ><a name="11930" class="Symbol"
+ >(</a
+ ><a name="11931" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#83" class="Datatype Operator"
+ >_≡_</a
+ ><a name="11934"
+ > </a
+ ><a name="11935" class="Symbol"
+ >{</a
+ ><a name="11936" class="Argument"
>A</a
- ><a name="11931"
+ ><a name="11937"
> </a
- ><a name="11932" class="Symbol"
+ ><a name="11938" class="Symbol"
>=</a
- ><a name="11933"
- > </a
- ><a name="11934" href="https://agda.github.io/agda-stdlib/Data.Maybe.Base.html#335" class="Datatype"
- >Maybe</a
><a name="11939"
> </a
- ><a name="11940" href="StlcProp.html#11899" class="Bound"
- >X</a
- ><a name="11941" class="Symbol"
- >}</a
- ><a name="11942"
+ ><a name="11940" href="https://agda.github.io/agda-stdlib/Data.Maybe.Base.html#335" class="Datatype"
+ >Maybe</a
+ ><a name="11945"
> </a
- ><a name="11943" class="Symbol"
- >(</a
- ><a name="11944" href="https://agda.github.io/agda-stdlib/Data.Maybe.Base.html#373" class="InductiveConstructor"
- >just</a
+ ><a name="11946" href="StlcProp.html#11905" class="Bound"
+ >X</a
+ ><a name="11947" class="Symbol"
+ >}</a
><a name="11948"
> </a
- ><a name="11949" href="StlcProp.html#11913" class="Bound"
- >x</a
- ><a name="11950" class="Symbol"
- >)</a
- ><a name="11951"
+ ><a name="11949" class="Symbol"
+ >(</a
+ ><a name="11950" href="https://agda.github.io/agda-stdlib/Data.Maybe.Base.html#373" class="InductiveConstructor"
+ >just</a
+ ><a name="11954"
> </a
- ><a name="11952" href="https://agda.github.io/agda-stdlib/Data.Maybe.Base.html#403" class="InductiveConstructor"
- >nothing</a
- ><a name="11959" class="Symbol"
+ ><a name="11955" href="StlcProp.html#11919" class="Bound"
+ >x</a
+ ><a name="11956" class="Symbol"
>)</a
- ><a name="11960"
+ ><a name="11957"
+ > </a
+ ><a name="11958" href="https://agda.github.io/agda-stdlib/Data.Maybe.Base.html#403" class="InductiveConstructor"
+ >nothing</a
+ ><a name="11965" class="Symbol"
+ >)</a
+ ><a name="11966"
>
</a
- ><a name="11961" href="StlcProp.html#11880" class="Function"
+ ><a name="11967" href="StlcProp.html#11886" class="Function"
>contradiction</a
- ><a name="11974"
+ ><a name="11980"
> </a
- ><a name="11975" class="Symbol"
+ ><a name="11981" class="Symbol"
>()</a
- ><a name="11977"
+ ><a name="11983"
>
</a
- ><a name="11979" href="StlcProp.html#11979" class="Function"
+ ><a name="11985" href="StlcProp.html#11985" class="Function"
>∅⊢-closed′</a
- ><a name="11989"
+ ><a name="11995"
> </a
- ><a name="11990" class="Symbol"
+ ><a name="11996" class="Symbol"
>:</a
- ><a name="11991"
+ ><a name="11997"
> </a
- ><a name="11992" class="Symbol"
- >∀</a
- ><a name="11993"
- > </a
- ><a name="11994" class="Symbol"
- >{</a
- ><a name="11995" href="StlcProp.html#11995" class="Bound"
- >M</a
- ><a name="11996"
- > </a
- ><a name="11997" href="StlcProp.html#11997" class="Bound"
- >A</a
><a name="11998" class="Symbol"
- >}</a
+ >∀</a
><a name="11999"
> </a
><a name="12000" class="Symbol"
- >→</a
- ><a name="12001"
+ >{</a
+ ><a name="12001" href="StlcProp.html#12001" class="Bound"
+ >M</a
+ ><a name="12002"
> </a
- ><a name="12002" href="Maps.html#10265" class="Function"
- >∅</a
- ><a name="12003"
- > </a
- ><a name="12004" href="Stlc.html#3112" class="Datatype Operator"
- >⊢</a
+ ><a name="12003" href="StlcProp.html#12003" class="Bound"
+ >A</a
+ ><a name="12004" class="Symbol"
+ >}</a
><a name="12005"
> </a
- ><a name="12006" href="StlcProp.html#11995" class="Bound"
- >M</a
+ ><a name="12006" class="Symbol"
+ >→</a
><a name="12007"
> </a
- ><a name="12008" href="Stlc.html#3112" class="Datatype Operator"
- >∶</a
+ ><a name="12008" href="Maps.html#10265" class="Function"
+ >∅</a
><a name="12009"
> </a
- ><a name="12010" href="StlcProp.html#11997" class="Bound"
- >A</a
+ ><a name="12010" href="Stlc.html#6070" class="Datatype Operator"
+ >⊢</a
><a name="12011"
> </a
- ><a name="12012" class="Symbol"
- >→</a
+ ><a name="12012" href="StlcProp.html#12001" class="Bound"
+ >M</a
><a name="12013"
> </a
- ><a name="12014" href="StlcProp.html#8176" class="Function"
- >closed</a
- ><a name="12020"
+ ><a name="12014" href="Stlc.html#6070" class="Datatype Operator"
+ >∶</a
+ ><a name="12015"
> </a
- ><a name="12021" href="StlcProp.html#11995" class="Bound"
- >M</a
- ><a name="12022"
- >
-</a
- ><a name="12023" href="StlcProp.html#11979" class="Function"
- >∅⊢-closed′</a
- ><a name="12033"
- > </a
- ><a name="12034" class="Symbol"
- >{</a
- ><a name="12035" href="StlcProp.html#12035" class="Bound"
- >M</a
- ><a name="12036" class="Symbol"
- >}</a
- ><a name="12037"
- > </a
- ><a name="12038" class="Symbol"
- >{</a
- ><a name="12039" href="StlcProp.html#12039" class="Bound"
+ ><a name="12016" href="StlcProp.html#12003" class="Bound"
>A</a
- ><a name="12040" class="Symbol"
- >}</a
- ><a name="12041"
+ ><a name="12017"
> </a
- ><a name="12042" href="StlcProp.html#12042" class="Bound"
- >⊢M</a
- ><a name="12044"
+ ><a name="12018" class="Symbol"
+ >→</a
+ ><a name="12019"
> </a
- ><a name="12045" class="Symbol"
- >{</a
- ><a name="12046" href="StlcProp.html#12046" class="Bound"
- >x</a
- ><a name="12047" class="Symbol"
- >}</a
- ><a name="12048"
+ ><a name="12020" href="StlcProp.html#8176" class="Function"
+ >closed</a
+ ><a name="12026"
> </a
- ><a name="12049" href="StlcProp.html#12049" class="Bound"
- >x∈M</a
- ><a name="12052"
- > </a
- ><a name="12053" class="Keyword"
- >with</a
- ><a name="12057"
- > </a
- ><a name="12058" href="StlcProp.html#9356" class="Function"
- >free-lemma</a
- ><a name="12068"
- > </a
- ><a name="12069" href="StlcProp.html#12049" class="Bound"
- >x∈M</a
- ><a name="12072"
- > </a
- ><a name="12073" href="StlcProp.html#12042" class="Bound"
- >⊢M</a
- ><a name="12075"
+ ><a name="12027" href="StlcProp.html#12001" class="Bound"
+ >M</a
+ ><a name="12028"
>
</a
- ><a name="12076" class="Symbol"
- >...</a
- ><a name="12079"
+ ><a name="12029" href="StlcProp.html#11985" class="Function"
+ >∅⊢-closed′</a
+ ><a name="12039"
> </a
- ><a name="12080" class="Symbol"
- >|</a
+ ><a name="12040" class="Symbol"
+ >{</a
+ ><a name="12041" href="StlcProp.html#12041" class="Bound"
+ >M</a
+ ><a name="12042" class="Symbol"
+ >}</a
+ ><a name="12043"
+ > </a
+ ><a name="12044" class="Symbol"
+ >{</a
+ ><a name="12045" href="StlcProp.html#12045" class="Bound"
+ >A</a
+ ><a name="12046" class="Symbol"
+ >}</a
+ ><a name="12047"
+ > </a
+ ><a name="12048" href="StlcProp.html#12048" class="Bound"
+ >⊢M</a
+ ><a name="12050"
+ > </a
+ ><a name="12051" class="Symbol"
+ >{</a
+ ><a name="12052" href="StlcProp.html#12052" class="Bound"
+ >x</a
+ ><a name="12053" class="Symbol"
+ >}</a
+ ><a name="12054"
+ > </a
+ ><a name="12055" href="StlcProp.html#12055" class="Bound"
+ >x∈M</a
+ ><a name="12058"
+ > </a
+ ><a name="12059" class="Keyword"
+ >with</a
+ ><a name="12063"
+ > </a
+ ><a name="12064" href="StlcProp.html#9356" class="Function"
+ >free-lemma</a
+ ><a name="12074"
+ > </a
+ ><a name="12075" href="StlcProp.html#12055" class="Bound"
+ >x∈M</a
+ ><a name="12078"
+ > </a
+ ><a name="12079" href="StlcProp.html#12048" class="Bound"
+ >⊢M</a
><a name="12081"
- > </a
+ >
+</a
><a name="12082" class="Symbol"
+ >...</a
+ ><a name="12085"
+ > </a
+ ><a name="12086" class="Symbol"
+ >|</a
+ ><a name="12087"
+ > </a
+ ><a name="12088" class="Symbol"
>(</a
- ><a name="12083" href="StlcProp.html#12083" class="Bound"
+ ><a name="12089" href="StlcProp.html#12089" class="Bound"
>B</a
- ><a name="12084"
+ ><a name="12090"
> </a
- ><a name="12085" href="https://agda.github.io/agda-stdlib/Data.Product.html#509" class="InductiveConstructor Operator"
+ ><a name="12091" href="https://agda.github.io/agda-stdlib/Data.Product.html#509" class="InductiveConstructor Operator"
>,</a
- ><a name="12086"
- > </a
- ><a name="12087" href="StlcProp.html#12087" class="Bound"
- >∅x≡B</a
- ><a name="12091" class="Symbol"
- >)</a
><a name="12092"
> </a
- ><a name="12093" class="Symbol"
- >=</a
- ><a name="12094"
- > </a
- ><a name="12095" href="StlcProp.html#11880" class="Function"
- >contradiction</a
- ><a name="12108"
- > </a
- ><a name="12109" class="Symbol"
- >(</a
- ><a name="12110" href="https://agda.github.io/agda-stdlib/Relation.Binary.PropositionalEquality.Core.html#632" class="Function"
- >trans</a
- ><a name="12115"
- > </a
- ><a name="12116" class="Symbol"
- >(</a
- ><a name="12117" href="https://agda.github.io/agda-stdlib/Relation.Binary.PropositionalEquality.Core.html#565" class="Function"
- >sym</a
- ><a name="12120"
- > </a
- ><a name="12121" href="StlcProp.html#12087" class="Bound"
+ ><a name="12093" href="StlcProp.html#12093" class="Bound"
>∅x≡B</a
- ><a name="12125" class="Symbol"
+ ><a name="12097" class="Symbol"
>)</a
+ ><a name="12098"
+ > </a
+ ><a name="12099" class="Symbol"
+ >=</a
+ ><a name="12100"
+ > </a
+ ><a name="12101" href="StlcProp.html#11886" class="Function"
+ >contradiction</a
+ ><a name="12114"
+ > </a
+ ><a name="12115" class="Symbol"
+ >(</a
+ ><a name="12116" href="https://agda.github.io/agda-stdlib/Relation.Binary.PropositionalEquality.Core.html#632" class="Function"
+ >trans</a
+ ><a name="12121"
+ > </a
+ ><a name="12122" class="Symbol"
+ >(</a
+ ><a name="12123" href="https://agda.github.io/agda-stdlib/Relation.Binary.PropositionalEquality.Core.html#565" class="Function"
+ >sym</a
><a name="12126"
> </a
- ><a name="12127" class="Symbol"
- >(</a
- ><a name="12128" href="Maps.html#10573" class="Function"
- >apply-∅</a
- ><a name="12135"
+ ><a name="12127" href="StlcProp.html#12093" class="Bound"
+ >∅x≡B</a
+ ><a name="12131" class="Symbol"
+ >)</a
+ ><a name="12132"
> </a
- ><a name="12136" href="StlcProp.html#12046" class="Bound"
+ ><a name="12133" class="Symbol"
+ >(</a
+ ><a name="12134" href="Maps.html#10573" class="Function"
+ >apply-∅</a
+ ><a name="12141"
+ > </a
+ ><a name="12142" href="StlcProp.html#12052" class="Bound"
>x</a
- ><a name="12137" class="Symbol"
+ ><a name="12143" class="Symbol"
>))</a
>
@@ -4002,144 +4002,144 @@ exchanged for the other.
<pre class="Agda">
-<a name="12491" href="StlcProp.html#12491" class="Function"
+<a name="12497" href="StlcProp.html#12497" class="Function"
>context-lemma</a
- ><a name="12504"
+ ><a name="12510"
> </a
- ><a name="12505" class="Symbol"
+ ><a name="12511" class="Symbol"
>:</a
- ><a name="12506"
+ ><a name="12512"
> </a
- ><a name="12507" class="Symbol"
+ ><a name="12513" class="Symbol"
>∀</a
- ><a name="12508"
- > </a
- ><a name="12509" class="Symbol"
- >{</a
- ><a name="12510" href="StlcProp.html#12510" class="Bound"
- >Γ</a
- ><a name="12511"
- > </a
- ><a name="12512" href="StlcProp.html#12512" class="Bound"
- >Γ′</a
><a name="12514"
> </a
- ><a name="12515" href="StlcProp.html#12515" class="Bound"
- >M</a
- ><a name="12516"
+ ><a name="12515" class="Symbol"
+ >{</a
+ ><a name="12516" href="StlcProp.html#12516" class="Bound"
+ >Γ</a
+ ><a name="12517"
> </a
- ><a name="12517" href="StlcProp.html#12517" class="Bound"
+ ><a name="12518" href="StlcProp.html#12518" class="Bound"
+ >Γ′</a
+ ><a name="12520"
+ > </a
+ ><a name="12521" href="StlcProp.html#12521" class="Bound"
+ >M</a
+ ><a name="12522"
+ > </a
+ ><a name="12523" href="StlcProp.html#12523" class="Bound"
>A</a
- ><a name="12518" class="Symbol"
+ ><a name="12524" class="Symbol"
>}</a
- ><a name="12519"
+ ><a name="12525"
>
</a
- ><a name="12528" class="Symbol"
+ ><a name="12534" class="Symbol"
>→</a
- ><a name="12529"
+ ><a name="12535"
> </a
- ><a name="12530" class="Symbol"
+ ><a name="12536" class="Symbol"
>(∀</a
- ><a name="12532"
- > </a
- ><a name="12533" class="Symbol"
- >{</a
- ><a name="12534" href="StlcProp.html#12534" class="Bound"
- >x</a
- ><a name="12535" class="Symbol"
- >}</a
- ><a name="12536"
- > </a
- ><a name="12537" class="Symbol"
- >→</a
><a name="12538"
> </a
- ><a name="12539" href="StlcProp.html#12534" class="Bound"
+ ><a name="12539" class="Symbol"
+ >{</a
+ ><a name="12540" href="StlcProp.html#12540" class="Bound"
>x</a
- ><a name="12540"
- > </a
- ><a name="12541" href="StlcProp.html#7659" class="Datatype Operator"
- >∈</a
+ ><a name="12541" class="Symbol"
+ >}</a
><a name="12542"
> </a
- ><a name="12543" href="StlcProp.html#12515" class="Bound"
- >M</a
+ ><a name="12543" class="Symbol"
+ >→</a
><a name="12544"
> </a
- ><a name="12545" class="Symbol"
- >→</a
+ ><a name="12545" href="StlcProp.html#12540" class="Bound"
+ >x</a
><a name="12546"
> </a
- ><a name="12547" href="StlcProp.html#12510" class="Bound"
- >Γ</a
+ ><a name="12547" href="StlcProp.html#7659" class="Datatype Operator"
+ >∈</a
><a name="12548"
> </a
- ><a name="12549" href="StlcProp.html#12534" class="Bound"
- >x</a
+ ><a name="12549" href="StlcProp.html#12521" class="Bound"
+ >M</a
><a name="12550"
> </a
- ><a name="12551" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#83" class="Datatype Operator"
- >≡</a
+ ><a name="12551" class="Symbol"
+ >→</a
><a name="12552"
> </a
- ><a name="12553" href="StlcProp.html#12512" class="Bound"
- >Γ′</a
- ><a name="12555"
- > </a
- ><a name="12556" href="StlcProp.html#12534" class="Bound"
- >x</a
- ><a name="12557" class="Symbol"
- >)</a
- ><a name="12558"
- >
- </a
- ><a name="12567" class="Symbol"
- >→</a
- ><a name="12568"
- > </a
- ><a name="12569" href="StlcProp.html#12510" class="Bound"
+ ><a name="12553" href="StlcProp.html#12516" class="Bound"
>Γ</a
- ><a name="12570"
- > </a
- ><a name="12572" href="Stlc.html#3112" class="Datatype Operator"
- >⊢</a
- ><a name="12573"
+ ><a name="12554"
> </a
- ><a name="12574" href="StlcProp.html#12515" class="Bound"
- >M</a
- ><a name="12575"
+ ><a name="12555" href="StlcProp.html#12540" class="Bound"
+ >x</a
+ ><a name="12556"
> </a
- ><a name="12576" href="Stlc.html#3112" class="Datatype Operator"
- >∶</a
- ><a name="12577"
+ ><a name="12557" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#83" class="Datatype Operator"
+ >≡</a
+ ><a name="12558"
> </a
- ><a name="12578" href="StlcProp.html#12517" class="Bound"
- >A</a
- ><a name="12579"
+ ><a name="12559" href="StlcProp.html#12518" class="Bound"
+ >Γ′</a
+ ><a name="12561"
+ > </a
+ ><a name="12562" href="StlcProp.html#12540" class="Bound"
+ >x</a
+ ><a name="12563" class="Symbol"
+ >)</a
+ ><a name="12564"
>
</a
- ><a name="12588" class="Symbol"
+ ><a name="12573" class="Symbol"
>→</a
- ><a name="12589"
+ ><a name="12574"
> </a
- ><a name="12590" href="StlcProp.html#12512" class="Bound"
- >Γ′</a
- ><a name="12592"
- > </a
- ><a name="12593" href="Stlc.html#3112" class="Datatype Operator"
+ ><a name="12575" href="StlcProp.html#12516" class="Bound"
+ >Γ</a
+ ><a name="12576"
+ > </a
+ ><a name="12578" href="Stlc.html#6070" class="Datatype Operator"
>⊢</a
- ><a name="12594"
+ ><a name="12579"
> </a
- ><a name="12595" href="StlcProp.html#12515" class="Bound"
+ ><a name="12580" href="StlcProp.html#12521" class="Bound"
>M</a
- ><a name="12596"
+ ><a name="12581"
> </a
- ><a name="12597" href="Stlc.html#3112" class="Datatype Operator"
+ ><a name="12582" href="Stlc.html#6070" class="Datatype Operator"
>∶</a
+ ><a name="12583"
+ > </a
+ ><a name="12584" href="StlcProp.html#12523" class="Bound"
+ >A</a
+ ><a name="12585"
+ >
+ </a
+ ><a name="12594" class="Symbol"
+ >→</a
+ ><a name="12595"
+ > </a
+ ><a name="12596" href="StlcProp.html#12518" class="Bound"
+ >Γ′</a
><a name="12598"
> </a
- ><a name="12599" href="StlcProp.html#12517" class="Bound"
+ ><a name="12599" href="Stlc.html#6070" class="Datatype Operator"
+ >⊢</a
+ ><a name="12600"
+ > </a
+ ><a name="12601" href="StlcProp.html#12521" class="Bound"
+ >M</a
+ ><a name="12602"
+ > </a
+ ><a name="12603" href="Stlc.html#6070" class="Datatype Operator"
+ >∶</a
+ ><a name="12604"
+ > </a
+ ><a name="12605" href="StlcProp.html#12523" class="Bound"
>A</a
>
@@ -4191,600 +4191,600 @@ _Proof_: By induction on the derivation of `Γ ⊢ M ∶ A`.
<pre class="Agda">
-<a name="14772" href="StlcProp.html#12491" class="Function"
+<a name="14778" href="StlcProp.html#12497" class="Function"
>context-lemma</a
- ><a name="14785"
+ ><a name="14791"
> </a
- ><a name="14786" href="StlcProp.html#14786" class="Bound"
+ ><a name="14792" href="StlcProp.html#14792" class="Bound"
>Γ~Γ′</a
- ><a name="14790"
+ ><a name="14796"
> </a
- ><a name="14791" class="Symbol"
+ ><a name="14797" class="Symbol"
>(</a
- ><a name="14792" href="Stlc.html#3156" class="InductiveConstructor"
+ ><a name="14798" href="Stlc.html#6114" class="InductiveConstructor"
>Ax</a
- ><a name="14794"
- > </a
- ><a name="14795" href="StlcProp.html#14795" class="Bound"
- >Γx≡A</a
- ><a name="14799" class="Symbol"
- >)</a
><a name="14800"
> </a
- ><a name="14801" class="Keyword"
- >rewrite</a
- ><a name="14808"
+ ><a name="14801" href="StlcProp.html#14801" class="Bound"
+ >Γx≡A</a
+ ><a name="14805" class="Symbol"
+ >)</a
+ ><a name="14806"
> </a
- ><a name="14809" class="Symbol"
- >(</a
- ><a name="14810" href="StlcProp.html#14786" class="Bound"
- >Γ~Γ′</a
+ ><a name="14807" class="Keyword"
+ >rewrite</a
><a name="14814"
> </a
- ><a name="14815" href="StlcProp.html#7689" class="InductiveConstructor"
+ ><a name="14815" class="Symbol"
+ >(</a
+ ><a name="14816" href="StlcProp.html#14792" class="Bound"
+ >Γ~Γ′</a
+ ><a name="14820"
+ > </a
+ ><a name="14821" href="StlcProp.html#7689" class="InductiveConstructor"
>free-`</a
- ><a name="14821" class="Symbol"
+ ><a name="14827" class="Symbol"
>)</a
- ><a name="14822"
+ ><a name="14828"
> </a
- ><a name="14823" class="Symbol"
+ ><a name="14829" class="Symbol"
>=</a
- ><a name="14824"
+ ><a name="14830"
> </a
- ><a name="14825" href="Stlc.html#3156" class="InductiveConstructor"
+ ><a name="14831" href="Stlc.html#6114" class="InductiveConstructor"
>Ax</a
- ><a name="14827"
+ ><a name="14833"
> </a
- ><a name="14828" href="StlcProp.html#14795" class="Bound"
+ ><a name="14834" href="StlcProp.html#14801" class="Bound"
>Γx≡A</a
- ><a name="14832"
+ ><a name="14838"
>
</a
- ><a name="14833" href="StlcProp.html#12491" class="Function"
+ ><a name="14839" href="StlcProp.html#12497" class="Function"
>context-lemma</a
- ><a name="14846"
+ ><a name="14852"
> </a
- ><a name="14847" class="Symbol"
+ ><a name="14853" class="Symbol"
>{</a
- ><a name="14848" href="StlcProp.html#14848" class="Bound"
+ ><a name="14854" href="StlcProp.html#14854" class="Bound"
>Γ</a
- ><a name="14849" class="Symbol"
+ ><a name="14855" class="Symbol"
>}</a
- ><a name="14850"
+ ><a name="14856"
> </a
- ><a name="14851" class="Symbol"
+ ><a name="14857" class="Symbol"
>{</a
- ><a name="14852" href="StlcProp.html#14852" class="Bound"
+ ><a name="14858" href="StlcProp.html#14858" class="Bound"
>Γ′</a
- ><a name="14854" class="Symbol"
+ ><a name="14860" class="Symbol"
>}</a
- ><a name="14855"
- > </a
- ><a name="14856" class="Symbol"
- >{</a
- ><a name="14857" href="Stlc.html#743" class="InductiveConstructor Operator"
- >λ[</a
- ><a name="14859"
- > </a
- ><a name="14860" href="StlcProp.html#14860" class="Bound"
- >x</a
><a name="14861"
> </a
- ><a name="14862" href="Stlc.html#743" class="InductiveConstructor Operator"
- >∶</a
- ><a name="14863"
- > </a
- ><a name="14864" href="StlcProp.html#14864" class="Bound"
- >A</a
+ ><a name="14862" class="Symbol"
+ >{</a
+ ><a name="14863" href="Stlc.html#3520" class="InductiveConstructor Operator"
+ >λ[</a
><a name="14865"
> </a
- ><a name="14866" href="Stlc.html#743" class="InductiveConstructor Operator"
- >]</a
+ ><a name="14866" href="StlcProp.html#14866" class="Bound"
+ >x</a
><a name="14867"
> </a
- ><a name="14868" href="StlcProp.html#14868" class="Bound"
+ ><a name="14868" href="Stlc.html#3520" class="InductiveConstructor Operator"
+ >∶</a
+ ><a name="14869"
+ > </a
+ ><a name="14870" href="StlcProp.html#14870" class="Bound"
+ >A</a
+ ><a name="14871"
+ > </a
+ ><a name="14872" href="Stlc.html#3520" class="InductiveConstructor Operator"
+ >]</a
+ ><a name="14873"
+ > </a
+ ><a name="14874" href="StlcProp.html#14874" class="Bound"
>N</a
- ><a name="14869" class="Symbol"
+ ><a name="14875" class="Symbol"
>}</a
- ><a name="14870"
+ ><a name="14876"
> </a
- ><a name="14871" href="StlcProp.html#14871" class="Bound"
+ ><a name="14877" href="StlcProp.html#14877" class="Bound"
>Γ~Γ′</a
- ><a name="14875"
+ ><a name="14881"
> </a
- ><a name="14876" class="Symbol"
+ ><a name="14882" class="Symbol"
>(</a
- ><a name="14877" href="Stlc.html#3210" class="InductiveConstructor"
+ ><a name="14883" href="Stlc.html#6168" class="InductiveConstructor"
>⇒-I</a
- ><a name="14880"
- > </a
- ><a name="14881" href="StlcProp.html#14881" class="Bound"
- >⊢N</a
- ><a name="14883" class="Symbol"
- >)</a
- ><a name="14884"
- > </a
- ><a name="14885" class="Symbol"
- >=</a
><a name="14886"
> </a
- ><a name="14887" href="Stlc.html#3210" class="InductiveConstructor"
- >⇒-I</a
+ ><a name="14887" href="StlcProp.html#14887" class="Bound"
+ >⊢N</a
+ ><a name="14889" class="Symbol"
+ >)</a
><a name="14890"
> </a
><a name="14891" class="Symbol"
+ >=</a
+ ><a name="14892"
+ > </a
+ ><a name="14893" href="Stlc.html#6168" class="InductiveConstructor"
+ >⇒-I</a
+ ><a name="14896"
+ > </a
+ ><a name="14897" class="Symbol"
>(</a
- ><a name="14892" href="StlcProp.html#12491" class="Function"
+ ><a name="14898" href="StlcProp.html#12497" class="Function"
>context-lemma</a
- ><a name="14905"
+ ><a name="14911"
> </a
- ><a name="14906" href="StlcProp.html#14927" class="Function"
+ ><a name="14912" href="StlcProp.html#14933" class="Function"
>Γx~Γ′x</a
- ><a name="14912"
+ ><a name="14918"
> </a
- ><a name="14913" href="StlcProp.html#14881" class="Bound"
+ ><a name="14919" href="StlcProp.html#14887" class="Bound"
>⊢N</a
- ><a name="14915" class="Symbol"
+ ><a name="14921" class="Symbol"
>)</a
- ><a name="14916"
+ ><a name="14922"
>
</a
- ><a name="14919" class="Keyword"
+ ><a name="14925" class="Keyword"
>where</a
- ><a name="14924"
+ ><a name="14930"
>
</a
- ><a name="14927" href="StlcProp.html#14927" class="Function"
+ ><a name="14933" href="StlcProp.html#14933" class="Function"
>Γx~Γ′x</a
- ><a name="14933"
+ ><a name="14939"
> </a
- ><a name="14934" class="Symbol"
- >:</a
- ><a name="14935"
- > </a
- ><a name="14936" class="Symbol"
- >∀</a
- ><a name="14937"
- > </a
- ><a name="14938" class="Symbol"
- >{</a
- ><a name="14939" href="StlcProp.html#14939" class="Bound"
- >y</a
><a name="14940" class="Symbol"
- >}</a
+ >:</a
><a name="14941"
> </a
><a name="14942" class="Symbol"
- >→</a
+ >∀</a
><a name="14943"
> </a
- ><a name="14944" href="StlcProp.html#14939" class="Bound"
+ ><a name="14944" class="Symbol"
+ >{</a
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>y</a
- ><a name="14945"
- > </a
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+ ><a name="14946" class="Symbol"
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><a name="14947"
> </a
- ><a name="14948" href="StlcProp.html#14868" class="Bound"
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> </a
- ><a name="14950" class="Symbol"
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+ ><a name="14950" href="StlcProp.html#14945" class="Bound"
+ >y</a
><a name="14951"
> </a
- ><a name="14952" class="Symbol"
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+ ><a name="14953"
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+ ><a name="14954" href="StlcProp.html#14874" class="Bound"
+ >N</a
+ ><a name="14955"
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><a name="14960"
> </a
- ><a name="14961" href="StlcProp.html#14864" class="Bound"
+ ><a name="14961" href="Maps.html#10368" class="Function Operator"
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+ ><a name="14962"
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+ ><a name="14963" href="StlcProp.html#14866" class="Bound"
+ >x</a
+ ><a name="14964"
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+ ><a name="14965" href="Maps.html#10368" class="Function Operator"
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+ ><a name="14966"
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> </a
- ><a name="14972" href="Maps.html#10368" class="Function Operator"
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> </a
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+ ><a name="14975" href="StlcProp.html#14858" class="Bound"
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- ><a name="14980"
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> </a
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- ><a name="14982"
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- </a
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- ><a name="14992" class="Symbol"
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- ><a name="15004"
- > </a
- ><a name="15005" href="StlcProp.html#14860" class="Bound"
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>x</a
- ><a name="15006"
+ ><a name="14981"
> </a
- ><a name="15007" href="Maps.html#2509" class="Function Operator"
- >≟</a
- ><a name="15008"
+ ><a name="14982" href="Maps.html#10368" class="Function Operator"
+ >∶</a
+ ><a name="14983"
> </a
- ><a name="15009" href="StlcProp.html#14993" class="Bound"
+ ><a name="14984" href="StlcProp.html#14870" class="Bound"
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+ ><a name="14985" class="Symbol"
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+ ><a name="14986"
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+ ><a name="14987" href="StlcProp.html#14945" class="Bound"
>y</a
- ><a name="15010"
+ ><a name="14988"
>
</a
- ><a name="15013" class="Symbol"
- >...</a
+ ><a name="14991" href="StlcProp.html#14933" class="Function"
+ >Γx~Γ′x</a
+ ><a name="14997"
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+ ><a name="14998" class="Symbol"
+ >{</a
+ ><a name="14999" href="StlcProp.html#14999" class="Bound"
+ >y</a
+ ><a name="15000" class="Symbol"
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+ ><a name="15001"
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+ ><a name="15002" href="StlcProp.html#15002" class="Bound"
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+ > </a
+ ><a name="15006" class="Keyword"
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+ ><a name="15012"
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+ ><a name="15013" href="Maps.html#2509" class="Function Operator"
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+ ><a name="15014"
+ > </a
+ ><a name="15015" href="StlcProp.html#14999" class="Bound"
+ >y</a
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+ </a
+ ><a name="15019" class="Symbol"
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> </a
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+ ><a name="15024"
> </a
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+ ><a name="15028"
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+ ><a name="15035"
> </a
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+ ><a name="15036" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#140" class="InductiveConstructor"
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>
</a
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- ><a name="15040"
+ ><a name="15046"
> </a
- ><a name="15041" class="Symbol"
+ ><a name="15047" class="Symbol"
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- ><a name="15042"
+ ><a name="15048"
> </a
- ><a name="15043" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#547" class="InductiveConstructor"
+ ><a name="15049" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#547" class="InductiveConstructor"
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> </a
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+ ><a name="15053" href="StlcProp.html#15053" class="Bound"
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+ ><a name="15056"
> </a
- ><a name="15052" class="Symbol"
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>=</a
- ><a name="15053"
+ ><a name="15059"
> </a
- ><a name="15054" href="StlcProp.html#14871" class="Bound"
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- ><a name="15058"
+ ><a name="15064"
> </a
- ><a name="15059" class="Symbol"
+ ><a name="15065" class="Symbol"
>(</a
- ><a name="15060" href="StlcProp.html#7717" class="InductiveConstructor"
+ ><a name="15066" href="StlcProp.html#7717" class="InductiveConstructor"
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+ ><a name="15072"
> </a
- ><a name="15067" href="StlcProp.html#15047" class="Bound"
+ ><a name="15073" href="StlcProp.html#15053" class="Bound"
>x≢y</a
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+ ><a name="15076"
> </a
- ><a name="15071" href="StlcProp.html#14996" class="Bound"
+ ><a name="15077" href="StlcProp.html#15002" class="Bound"
>y∈N</a
- ><a name="15074" class="Symbol"
+ ><a name="15080" class="Symbol"
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- ><a name="15075"
+ ><a name="15081"
>
</a
- ><a name="15076" href="StlcProp.html#12491" class="Function"
+ ><a name="15082" href="StlcProp.html#12497" class="Function"
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> </a
- ><a name="15090" href="StlcProp.html#15090" class="Bound"
+ ><a name="15096" href="StlcProp.html#15096" class="Bound"
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- ><a name="15094"
+ ><a name="15100"
> </a
- ><a name="15095" class="Symbol"
+ ><a name="15101" class="Symbol"
>(</a
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+ ><a name="15102" href="Stlc.html#6245" class="InductiveConstructor"
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> </a
- ><a name="15100" href="StlcProp.html#15100" class="Bound"
+ ><a name="15106" href="StlcProp.html#15106" class="Bound"
>⊢L</a
- ><a name="15102"
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- ><a name="15103" href="StlcProp.html#15103" class="Bound"
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- ><a name="15105" class="Symbol"
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- ><a name="15106"
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><a name="15108"
> </a
- ><a name="15109" href="Stlc.html#3287" class="InductiveConstructor"
- >⇒-E</a
+ ><a name="15109" href="StlcProp.html#15109" class="Bound"
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+ ><a name="15111" class="Symbol"
+ >)</a
><a name="15112"
> </a
><a name="15113" class="Symbol"
- >(</a
- ><a name="15114" href="StlcProp.html#12491" class="Function"
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+ >=</a
+ ><a name="15114"
> </a
- ><a name="15128" class="Symbol"
+ ><a name="15115" href="Stlc.html#6245" class="InductiveConstructor"
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+ ><a name="15118"
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+ ><a name="15119" class="Symbol"
>(</a
- ><a name="15129" href="StlcProp.html#15090" class="Bound"
- >Γ~Γ′</a
+ ><a name="15120" href="StlcProp.html#12497" class="Function"
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><a name="15133"
> </a
- ><a name="15134" href="https://agda.github.io/agda-stdlib/Function.html#713" class="Function Operator"
- >∘</a
- ><a name="15135"
+ ><a name="15134" class="Symbol"
+ >(</a
+ ><a name="15135" href="StlcProp.html#15096" class="Bound"
+ >Γ~Γ′</a
+ ><a name="15139"
> </a
- ><a name="15136" href="StlcProp.html#7778" class="InductiveConstructor"
+ ><a name="15140" href="https://agda.github.io/agda-stdlib/Function.html#713" class="Function Operator"
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+ ><a name="15141"
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+ ><a name="15142" href="StlcProp.html#7778" class="InductiveConstructor"
>free-·₁</a
- ><a name="15143" class="Symbol"
+ ><a name="15149" class="Symbol"
>)</a
- ><a name="15144"
+ ><a name="15150"
> </a
- ><a name="15146" href="StlcProp.html#15100" class="Bound"
+ ><a name="15152" href="StlcProp.html#15106" class="Bound"
>⊢L</a
- ><a name="15148" class="Symbol"
+ ><a name="15154" class="Symbol"
>)</a
- ><a name="15149"
+ ><a name="15155"
>
</a
- ><a name="15189" class="Symbol"
+ ><a name="15195" class="Symbol"
>(</a
- ><a name="15190" href="StlcProp.html#12491" class="Function"
+ ><a name="15196" href="StlcProp.html#12497" class="Function"
>context-lemma</a
- ><a name="15203"
- > </a
- ><a name="15204" class="Symbol"
- >(</a
- ><a name="15205" href="StlcProp.html#15090" class="Bound"
- >Γ~Γ′</a
><a name="15209"
> </a
- ><a name="15210" href="https://agda.github.io/agda-stdlib/Function.html#713" class="Function Operator"
+ ><a name="15210" class="Symbol"
+ >(</a
+ ><a name="15211" href="StlcProp.html#15096" class="Bound"
+ >Γ~Γ′</a
+ ><a name="15215"
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+ ><a name="15216" href="https://agda.github.io/agda-stdlib/Function.html#713" class="Function Operator"
>∘</a
- ><a name="15211"
+ ><a name="15217"
> </a
- ><a name="15212" href="StlcProp.html#7822" class="InductiveConstructor"
+ ><a name="15218" href="StlcProp.html#7822" class="InductiveConstructor"
>free-·₂</a
- ><a name="15219" class="Symbol"
+ ><a name="15225" class="Symbol"
>)</a
- ><a name="15220"
+ ><a name="15226"
> </a
- ><a name="15221" href="StlcProp.html#15103" class="Bound"
+ ><a name="15227" href="StlcProp.html#15109" class="Bound"
>⊢M</a
- ><a name="15223" class="Symbol"
+ ><a name="15229" class="Symbol"
>)</a
- ><a name="15224"
+ ><a name="15230"
>
</a
- ><a name="15226" href="StlcProp.html#12491" class="Function"
+ ><a name="15232" href="StlcProp.html#12497" class="Function"
>context-lemma</a
- ><a name="15239"
+ ><a name="15245"
> </a
- ><a name="15240" href="StlcProp.html#15240" class="Bound"
+ ><a name="15246" href="StlcProp.html#15246" class="Bound"
>Γ~Γ′</a
- ><a name="15244"
+ ><a name="15250"
> </a
- ><a name="15245" href="Stlc.html#3365" class="InductiveConstructor"
+ ><a name="15251" href="Stlc.html#6323" class="InductiveConstructor"
>𝔹-I₁</a
- ><a name="15249"
+ ><a name="15255"
> </a
- ><a name="15250" class="Symbol"
+ ><a name="15256" class="Symbol"
>=</a
- ><a name="15251"
+ ><a name="15257"
> </a
- ><a name="15252" href="Stlc.html#3365" class="InductiveConstructor"
+ ><a name="15258" href="Stlc.html#6323" class="InductiveConstructor"
>𝔹-I₁</a
- ><a name="15256"
+ ><a name="15262"
>
</a
- ><a name="15257" href="StlcProp.html#12491" class="Function"
+ ><a name="15263" href="StlcProp.html#12497" class="Function"
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- ><a name="15270"
+ ><a name="15276"
> </a
- ><a name="15271" href="StlcProp.html#15271" class="Bound"
+ ><a name="15277" href="StlcProp.html#15277" class="Bound"
>Γ~Γ′</a
- ><a name="15275"
+ ><a name="15281"
> </a
- ><a name="15276" href="Stlc.html#3399" class="InductiveConstructor"
+ ><a name="15282" href="Stlc.html#6357" class="InductiveConstructor"
>𝔹-I₂</a
- ><a name="15280"
+ ><a name="15286"
> </a
- ><a name="15281" class="Symbol"
+ ><a name="15287" class="Symbol"
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- ><a name="15282"
+ ><a name="15288"
> </a
- ><a name="15283" href="Stlc.html#3399" class="InductiveConstructor"
+ ><a name="15289" href="Stlc.html#6357" class="InductiveConstructor"
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- ><a name="15287"
+ ><a name="15293"
>
</a
- ><a name="15288" href="StlcProp.html#12491" class="Function"
+ ><a name="15294" href="StlcProp.html#12497" class="Function"
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- ><a name="15301"
+ ><a name="15307"
> </a
- ><a name="15302" href="StlcProp.html#15302" class="Bound"
+ ><a name="15308" href="StlcProp.html#15308" class="Bound"
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- ><a name="15306"
+ ><a name="15312"
> </a
- ><a name="15307" class="Symbol"
+ ><a name="15313" class="Symbol"
>(</a
- ><a name="15308" href="Stlc.html#3434" class="InductiveConstructor"
+ ><a name="15314" href="Stlc.html#6392" class="InductiveConstructor"
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- ><a name="15311"
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- ><a name="15312" href="StlcProp.html#15312" class="Bound"
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- ><a name="15314"
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- ><a name="15315" href="StlcProp.html#15315" class="Bound"
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><a name="15317"
> </a
><a name="15318" href="StlcProp.html#15318" class="Bound"
- >⊢N</a
- ><a name="15320" class="Symbol"
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- ><a name="15321"
+ >⊢L</a
+ ><a name="15320"
> </a
- ><a name="15322" class="Symbol"
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+ ><a name="15321" href="StlcProp.html#15321" class="Bound"
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> </a
- ><a name="15324" href="Stlc.html#3434" class="InductiveConstructor"
- >𝔹-E</a
+ ><a name="15324" href="StlcProp.html#15324" class="Bound"
+ >⊢N</a
+ ><a name="15326" class="Symbol"
+ >)</a
><a name="15327"
> </a
><a name="15328" class="Symbol"
- >(</a
- ><a name="15329" href="StlcProp.html#12491" class="Function"
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- ><a name="15342"
+ >=</a
+ ><a name="15329"
> </a
- ><a name="15343" class="Symbol"
+ ><a name="15330" href="Stlc.html#6392" class="InductiveConstructor"
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+ ><a name="15333"
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+ ><a name="15334" class="Symbol"
>(</a
- ><a name="15344" href="StlcProp.html#15302" class="Bound"
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+ ><a name="15335" href="StlcProp.html#12497" class="Function"
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><a name="15348"
> </a
- ><a name="15349" href="https://agda.github.io/agda-stdlib/Function.html#713" class="Function Operator"
+ ><a name="15349" class="Symbol"
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+ ><a name="15350" href="StlcProp.html#15308" class="Bound"
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+ ><a name="15354"
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+ ><a name="15355" href="https://agda.github.io/agda-stdlib/Function.html#713" class="Function Operator"
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- ><a name="15350"
+ ><a name="15356"
> </a
- ><a name="15351" href="StlcProp.html#7866" class="InductiveConstructor"
+ ><a name="15357" href="StlcProp.html#7866" class="InductiveConstructor"
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- ><a name="15359" class="Symbol"
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- ><a name="15360"
+ ><a name="15366"
> </a
- ><a name="15361" href="StlcProp.html#15312" class="Bound"
+ ><a name="15367" href="StlcProp.html#15318" class="Bound"
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- ><a name="15363" class="Symbol"
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- ><a name="15364"
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</a
- ><a name="15406" class="Symbol"
+ ><a name="15412" class="Symbol"
>(</a
- ><a name="15407" href="StlcProp.html#12491" class="Function"
+ ><a name="15413" href="StlcProp.html#12497" class="Function"
>context-lemma</a
- ><a name="15420"
- > </a
- ><a name="15421" class="Symbol"
- >(</a
- ><a name="15422" href="StlcProp.html#15302" class="Bound"
- >Γ~Γ′</a
><a name="15426"
> </a
- ><a name="15427" href="https://agda.github.io/agda-stdlib/Function.html#713" class="Function Operator"
+ ><a name="15427" class="Symbol"
+ >(</a
+ ><a name="15428" href="StlcProp.html#15308" class="Bound"
+ >Γ~Γ′</a
+ ><a name="15432"
+ > </a
+ ><a name="15433" href="https://agda.github.io/agda-stdlib/Function.html#713" class="Function Operator"
>∘</a
- ><a name="15428"
+ ><a name="15434"
> </a
- ><a name="15429" href="StlcProp.html#7926" class="InductiveConstructor"
+ ><a name="15435" href="StlcProp.html#7926" class="InductiveConstructor"
>free-if₂</a
- ><a name="15437" class="Symbol"
+ ><a name="15443" class="Symbol"
>)</a
- ><a name="15438"
+ ><a name="15444"
> </a
- ><a name="15439" href="StlcProp.html#15315" class="Bound"
+ ><a name="15445" href="StlcProp.html#15321" class="Bound"
>⊢M</a
- ><a name="15441" class="Symbol"
+ ><a name="15447" class="Symbol"
>)</a
- ><a name="15442"
+ ><a name="15448"
>
</a
- ><a name="15484" class="Symbol"
+ ><a name="15490" class="Symbol"
>(</a
- ><a name="15485" href="StlcProp.html#12491" class="Function"
+ ><a name="15491" href="StlcProp.html#12497" class="Function"
>context-lemma</a
- ><a name="15498"
- > </a
- ><a name="15499" class="Symbol"
- >(</a
- ><a name="15500" href="StlcProp.html#15302" class="Bound"
- >Γ~Γ′</a
><a name="15504"
> </a
- ><a name="15505" href="https://agda.github.io/agda-stdlib/Function.html#713" class="Function Operator"
+ ><a name="15505" class="Symbol"
+ >(</a
+ ><a name="15506" href="StlcProp.html#15308" class="Bound"
+ >Γ~Γ′</a
+ ><a name="15510"
+ > </a
+ ><a name="15511" href="https://agda.github.io/agda-stdlib/Function.html#713" class="Function Operator"
>∘</a
- ><a name="15506"
+ ><a name="15512"
> </a
- ><a name="15507" href="StlcProp.html#7986" class="InductiveConstructor"
+ ><a name="15513" href="StlcProp.html#7986" class="InductiveConstructor"
>free-if₃</a
- ><a name="15515" class="Symbol"
+ ><a name="15521" class="Symbol"
>)</a
- ><a name="15516"
+ ><a name="15522"
> </a
- ><a name="15517" href="StlcProp.html#15318" class="Bound"
+ ><a name="15523" href="StlcProp.html#15324" class="Bound"
>⊢N</a
- ><a name="15519" class="Symbol"
+ ><a name="15525" class="Symbol"
>)</a
>
@@ -4809,162 +4809,162 @@ _Lemma_: If `Γ , x ∶ A ⊢ N ∶ B` and `∅ ⊢ V ∶ A`, then
<pre class="Agda">
-<a name="16218" href="StlcProp.html#16218" class="Function"
+<a name="16224" href="StlcProp.html#16224" class="Function"
>preservation-[:=]</a
- ><a name="16235"
+ ><a name="16241"
> </a
- ><a name="16236" class="Symbol"
+ ><a name="16242" class="Symbol"
>:</a
- ><a name="16237"
+ ><a name="16243"
> </a
- ><a name="16238" class="Symbol"
+ ><a name="16244" class="Symbol"
>∀</a
- ><a name="16239"
+ ><a name="16245"
> </a
- ><a name="16240" class="Symbol"
+ ><a name="16246" class="Symbol"
>{</a
- ><a name="16241" href="StlcProp.html#16241" class="Bound"
- >Γ</a
- ><a name="16242"
- > </a
- ><a name="16243" href="StlcProp.html#16243" class="Bound"
- >x</a
- ><a name="16244"
- > </a
- ><a name="16245" href="StlcProp.html#16245" class="Bound"
- >A</a
- ><a name="16246"
- > </a
><a name="16247" href="StlcProp.html#16247" class="Bound"
- >N</a
+ >Γ</a
><a name="16248"
> </a
><a name="16249" href="StlcProp.html#16249" class="Bound"
- >B</a
+ >x</a
><a name="16250"
> </a
><a name="16251" href="StlcProp.html#16251" class="Bound"
+ >A</a
+ ><a name="16252"
+ > </a
+ ><a name="16253" href="StlcProp.html#16253" class="Bound"
+ >N</a
+ ><a name="16254"
+ > </a
+ ><a name="16255" href="StlcProp.html#16255" class="Bound"
+ >B</a
+ ><a name="16256"
+ > </a
+ ><a name="16257" href="StlcProp.html#16257" class="Bound"
>V</a
- ><a name="16252" class="Symbol"
+ ><a name="16258" class="Symbol"
>}</a
- ><a name="16253"
+ ><a name="16259"
>
</a
- ><a name="16271" class="Symbol"
+ ><a name="16277" class="Symbol"
>→</a
- ><a name="16272"
+ ><a name="16278"
> </a
- ><a name="16273" class="Symbol"
+ ><a name="16279" class="Symbol"
>(</a
- ><a name="16274" href="StlcProp.html#16241" class="Bound"
+ ><a name="16280" href="StlcProp.html#16247" class="Bound"
>Γ</a
- ><a name="16275"
- > </a
- ><a name="16276" href="Maps.html#10368" class="Function Operator"
- >,</a
- ><a name="16277"
- > </a
- ><a name="16278" href="StlcProp.html#16243" class="Bound"
- >x</a
- ><a name="16279"
- > </a
- ><a name="16280" href="Maps.html#10368" class="Function Operator"
- >∶</a
><a name="16281"
> </a
- ><a name="16282" href="StlcProp.html#16245" class="Bound"
- >A</a
- ><a name="16283" class="Symbol"
- >)</a
- ><a name="16284"
+ ><a name="16282" href="Maps.html#10368" class="Function Operator"
+ >,</a
+ ><a name="16283"
> </a
- ><a name="16285" href="Stlc.html#3112" class="Datatype Operator"
- >⊢</a
- ><a name="16286"
+ ><a name="16284" href="StlcProp.html#16249" class="Bound"
+ >x</a
+ ><a name="16285"
> </a
- ><a name="16287" href="StlcProp.html#16247" class="Bound"
- >N</a
- ><a name="16288"
- > </a
- ><a name="16289" href="Stlc.html#3112" class="Datatype Operator"
+ ><a name="16286" href="Maps.html#10368" class="Function Operator"
>∶</a
+ ><a name="16287"
+ > </a
+ ><a name="16288" href="StlcProp.html#16251" class="Bound"
+ >A</a
+ ><a name="16289" class="Symbol"
+ >)</a
><a name="16290"
> </a
- ><a name="16291" href="StlcProp.html#16249" class="Bound"
- >B</a
+ ><a name="16291" href="Stlc.html#6070" class="Datatype Operator"
+ >⊢</a
><a name="16292"
+ > </a
+ ><a name="16293" href="StlcProp.html#16253" class="Bound"
+ >N</a
+ ><a name="16294"
+ > </a
+ ><a name="16295" href="Stlc.html#6070" class="Datatype Operator"
+ >∶</a
+ ><a name="16296"
+ > </a
+ ><a name="16297" href="StlcProp.html#16255" class="Bound"
+ >B</a
+ ><a name="16298"
>
</a
- ><a name="16310" class="Symbol"
+ ><a name="16316" class="Symbol"
>→</a
- ><a name="16311"
- > </a
- ><a name="16312" href="Maps.html#10265" class="Function"
- >∅</a
- ><a name="16313"
- > </a
- ><a name="16314" href="Stlc.html#3112" class="Datatype Operator"
- >⊢</a
- ><a name="16315"
- > </a
- ><a name="16316" href="StlcProp.html#16251" class="Bound"
- >V</a
><a name="16317"
> </a
- ><a name="16318" href="Stlc.html#3112" class="Datatype Operator"
- >∶</a
+ ><a name="16318" href="Maps.html#10265" class="Function"
+ >∅</a
><a name="16319"
> </a
- ><a name="16320" href="StlcProp.html#16245" class="Bound"
- >A</a
+ ><a name="16320" href="Stlc.html#6070" class="Datatype Operator"
+ >⊢</a
><a name="16321"
+ > </a
+ ><a name="16322" href="StlcProp.html#16257" class="Bound"
+ >V</a
+ ><a name="16323"
+ > </a
+ ><a name="16324" href="Stlc.html#6070" class="Datatype Operator"
+ >∶</a
+ ><a name="16325"
+ > </a
+ ><a name="16326" href="StlcProp.html#16251" class="Bound"
+ >A</a
+ ><a name="16327"
>
</a
- ><a name="16339" class="Symbol"
- >→</a
- ><a name="16340"
- > </a
- ><a name="16341" href="StlcProp.html#16241" class="Bound"
- >Γ</a
- ><a name="16342"
- > </a
- ><a name="16343" href="Stlc.html#3112" class="Datatype Operator"
- >⊢</a
- ><a name="16344"
- > </a
><a name="16345" class="Symbol"
+ >→</a
+ ><a name="16346"
+ > </a
+ ><a name="16347" href="StlcProp.html#16247" class="Bound"
+ >Γ</a
+ ><a name="16348"
+ > </a
+ ><a name="16349" href="Stlc.html#6070" class="Datatype Operator"
+ >⊢</a
+ ><a name="16350"
+ > </a
+ ><a name="16351" class="Symbol"
>(</a
- ><a name="16346" href="StlcProp.html#16247" class="Bound"
+ ><a name="16352" href="StlcProp.html#16253" class="Bound"
>N</a
- ><a name="16347"
+ ><a name="16353"
> </a
- ><a name="16348" href="Stlc.html#1276" class="Function Operator"
+ ><a name="16354" href="Stlc.html#4234" class="Function Operator"
>[</a
- ><a name="16349"
+ ><a name="16355"
> </a
- ><a name="16350" href="StlcProp.html#16243" class="Bound"
+ ><a name="16356" href="StlcProp.html#16249" class="Bound"
>x</a
- ><a name="16351"
+ ><a name="16357"
> </a
- ><a name="16352" href="Stlc.html#1276" class="Function Operator"
+ ><a name="16358" href="Stlc.html#4234" class="Function Operator"
>:=</a
- ><a name="16354"
+ ><a name="16360"
> </a
- ><a name="16355" href="StlcProp.html#16251" class="Bound"
+ ><a name="16361" href="StlcProp.html#16257" class="Bound"
>V</a
- ><a name="16356"
+ ><a name="16362"
> </a
- ><a name="16357" href="Stlc.html#1276" class="Function Operator"
+ ><a name="16363" href="Stlc.html#4234" class="Function Operator"
>]</a
- ><a name="16358" class="Symbol"
+ ><a name="16364" class="Symbol"
>)</a
- ><a name="16359"
+ ><a name="16365"
> </a
- ><a name="16360" href="Stlc.html#3112" class="Datatype Operator"
+ ><a name="16366" href="Stlc.html#6070" class="Datatype Operator"
>∶</a
- ><a name="16361"
+ ><a name="16367"
> </a
- ><a name="16362" href="StlcProp.html#16249" class="Bound"
+ ><a name="16368" href="StlcProp.html#16255" class="Bound"
>B</a
>
@@ -4994,7 +4994,7 @@ we show that if `∅ ⊢ V ∶ A` then `Γ ⊢ N [ x := V ] ∶ B`.
- If `N` is a variable there are two cases to consider,
depending on whether `N` is `x` or some other variable.
- - If `N = \` x`, then from `Γ , x ∶ A ⊢ x ∶ B`
+ - If `N = `` `x ``, then from `Γ , x ∶ A ⊢ x ∶ B`
we know that looking up `x` in `Γ , x : A` gives
`just B`, but we already know it gives `just A`;
applying injectivity for `just` we conclude that `A ≡ B`.
@@ -5038,381 +5038,369 @@ we show that if `∅ ⊢ V ∶ A` then `Γ ⊢ N [ x := V ] ∶ B`.
We need a couple of lemmas. A closed term can be weakened to any context, and `just` is injective.
<pre class="Agda">
-<a name="19516" href="StlcProp.html#19516" class="Function"
+<a name="19525" href="StlcProp.html#19525" class="Function"
>weaken-closed</a
- ><a name="19529"
- > </a
- ><a name="19530" class="Symbol"
- >:</a
- ><a name="19531"
- > </a
- ><a name="19532" class="Symbol"
- >∀</a
- ><a name="19533"
- > </a
- ><a name="19534" class="Symbol"
- >{</a
- ><a name="19535" href="StlcProp.html#19535" class="Bound"
- >V</a
- ><a name="19536"
- > </a
- ><a name="19537" href="StlcProp.html#19537" class="Bound"
- >A</a
><a name="19538"
> </a
- ><a name="19539" href="StlcProp.html#19539" class="Bound"
- >Γ</a
- ><a name="19540" class="Symbol"
- >}</a
- ><a name="19541"
+ ><a name="19539" class="Symbol"
+ >:</a
+ ><a name="19540"
> </a
- ><a name="19542" class="Symbol"
- >→</a
- ><a name="19543"
+ ><a name="19541" class="Symbol"
+ >∀</a
+ ><a name="19542"
> </a
- ><a name="19544" href="Maps.html#10265" class="Function"
- >∅</a
+ ><a name="19543" class="Symbol"
+ >{</a
+ ><a name="19544" href="StlcProp.html#19544" class="Bound"
+ >V</a
><a name="19545"
> </a
- ><a name="19546" href="Stlc.html#3112" class="Datatype Operator"
- >⊢</a
+ ><a name="19546" href="StlcProp.html#19546" class="Bound"
+ >A</a
><a name="19547"
> </a
- ><a name="19548" href="StlcProp.html#19535" class="Bound"
- >V</a
- ><a name="19549"
- > </a
- ><a name="19550" href="Stlc.html#3112" class="Datatype Operator"
- >∶</a
- ><a name="19551"
- > </a
- ><a name="19552" href="StlcProp.html#19537" class="Bound"
- >A</a
- ><a name="19553"
- > </a
- ><a name="19554" class="Symbol"
- >→</a
- ><a name="19555"
- > </a
- ><a name="19556" href="StlcProp.html#19539" class="Bound"
+ ><a name="19548" href="StlcProp.html#19548" class="Bound"
>Γ</a
- ><a name="19557"
+ ><a name="19549" class="Symbol"
+ >}</a
+ ><a name="19550"
> </a
- ><a name="19558" href="Stlc.html#3112" class="Datatype Operator"
+ ><a name="19551" class="Symbol"
+ >→</a
+ ><a name="19552"
+ > </a
+ ><a name="19553" href="Maps.html#10265" class="Function"
+ >∅</a
+ ><a name="19554"
+ > </a
+ ><a name="19555" href="Stlc.html#6070" class="Datatype Operator"
>⊢</a
- ><a name="19559"
+ ><a name="19556"
> </a
- ><a name="19560" href="StlcProp.html#19535" class="Bound"
+ ><a name="19557" href="StlcProp.html#19544" class="Bound"
>V</a
- ><a name="19561"
+ ><a name="19558"
> </a
- ><a name="19562" href="Stlc.html#3112" class="Datatype Operator"
+ ><a name="19559" href="Stlc.html#6070" class="Datatype Operator"
>∶</a
- ><a name="19563"
+ ><a name="19560"
> </a
- ><a name="19564" href="StlcProp.html#19537" class="Bound"
+ ><a name="19561" href="StlcProp.html#19546" class="Bound"
>A</a
- ><a name="19565"
+ ><a name="19562"
+ > </a
+ ><a name="19563" class="Symbol"
+ >→</a
+ ><a name="19564"
+ > </a
+ ><a name="19565" href="StlcProp.html#19548" class="Bound"
+ >Γ</a
+ ><a name="19566"
+ > </a
+ ><a name="19567" href="Stlc.html#6070" class="Datatype Operator"
+ >⊢</a
+ ><a name="19568"
+ > </a
+ ><a name="19569" href="StlcProp.html#19544" class="Bound"
+ >V</a
+ ><a name="19570"
+ > </a
+ ><a name="19571" href="Stlc.html#6070" class="Datatype Operator"
+ >∶</a
+ ><a name="19572"
+ > </a
+ ><a name="19573" href="StlcProp.html#19546" class="Bound"
+ >A</a
+ ><a name="19574"
>
</a
- ><a name="19566" href="StlcProp.html#19516" class="Function"
+ ><a name="19575" href="StlcProp.html#19525" class="Function"
>weaken-closed</a
- ><a name="19579"
+ ><a name="19588"
> </a
- ><a name="19580" class="Symbol"
+ ><a name="19589" class="Symbol"
>{</a
- ><a name="19581" href="StlcProp.html#19581" class="Bound"
+ ><a name="19590" href="StlcProp.html#19590" class="Bound"
>V</a
- ><a name="19582" class="Symbol"
+ ><a name="19591" class="Symbol"
>}</a
- ><a name="19583"
+ ><a name="19592"
> </a
- ><a name="19584" class="Symbol"
+ ><a name="19593" class="Symbol"
>{</a
- ><a name="19585" href="StlcProp.html#19585" class="Bound"
+ ><a name="19594" href="StlcProp.html#19594" class="Bound"
>A</a
- ><a name="19586" class="Symbol"
- >}</a
- ><a name="19587"
- > </a
- ><a name="19588" class="Symbol"
- >{</a
- ><a name="19589" href="StlcProp.html#19589" class="Bound"
- >Γ</a
- ><a name="19590" class="Symbol"
- >}</a
- ><a name="19591"
- > </a
- ><a name="19592" href="StlcProp.html#19592" class="Bound"
- >⊢V</a
- ><a name="19594"
- > </a
><a name="19595" class="Symbol"
- >=</a
+ >}</a
><a name="19596"
> </a
- ><a name="19597" href="StlcProp.html#12491" class="Function"
- >context-lemma</a
- ><a name="19610"
- > </a
- ><a name="19611" href="StlcProp.html#19629" class="Function"
- >Γ~Γ′</a
- ><a name="19615"
- > </a
- ><a name="19616" href="StlcProp.html#19592" class="Bound"
- >⊢V</a
- ><a name="19618"
- >
- </a
- ><a name="19621" class="Keyword"
- >where</a
- ><a name="19626"
- >
- </a
- ><a name="19629" href="StlcProp.html#19629" class="Function"
- >Γ~Γ′</a
- ><a name="19633"
- > </a
- ><a name="19634" class="Symbol"
- >:</a
- ><a name="19635"
- > </a
- ><a name="19636" class="Symbol"
- >∀</a
- ><a name="19637"
- > </a
- ><a name="19638" class="Symbol"
+ ><a name="19597" class="Symbol"
>{</a
- ><a name="19639" href="StlcProp.html#19639" class="Bound"
- >x</a
- ><a name="19640" class="Symbol"
- >}</a
- ><a name="19641"
- > </a
- ><a name="19642" class="Symbol"
- >→</a
- ><a name="19643"
- > </a
- ><a name="19644" href="StlcProp.html#19639" class="Bound"
- >x</a
- ><a name="19645"
- > </a
- ><a name="19646" href="StlcProp.html#7659" class="Datatype Operator"
- >∈</a
- ><a name="19647"
- > </a
- ><a name="19648" href="StlcProp.html#19581" class="Bound"
- >V</a
- ><a name="19649"
- > </a
- ><a name="19650" class="Symbol"
- >→</a
- ><a name="19651"
- > </a
- ><a name="19652" href="Maps.html#10265" class="Function"
- >∅</a
- ><a name="19653"
- > </a
- ><a name="19654" href="StlcProp.html#19639" class="Bound"
- >x</a
- ><a name="19655"
- > </a
- ><a name="19656" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#83" class="Datatype Operator"
- >≡</a
- ><a name="19657"
- > </a
- ><a name="19658" href="StlcProp.html#19589" class="Bound"
+ ><a name="19598" href="StlcProp.html#19598" class="Bound"
>Γ</a
- ><a name="19659"
+ ><a name="19599" class="Symbol"
+ >}</a
+ ><a name="19600"
> </a
- ><a name="19660" href="StlcProp.html#19639" class="Bound"
- >x</a
- ><a name="19661"
+ ><a name="19601" href="StlcProp.html#19601" class="Bound"
+ >⊢V</a
+ ><a name="19603"
+ > </a
+ ><a name="19604" class="Symbol"
+ >=</a
+ ><a name="19605"
+ > </a
+ ><a name="19606" href="StlcProp.html#12497" class="Function"
+ >context-lemma</a
+ ><a name="19619"
+ > </a
+ ><a name="19620" href="StlcProp.html#19638" class="Function"
+ >Γ~Γ′</a
+ ><a name="19624"
+ > </a
+ ><a name="19625" href="StlcProp.html#19601" class="Bound"
+ >⊢V</a
+ ><a name="19627"
>
</a
- ><a name="19664" href="StlcProp.html#19629" class="Function"
+ ><a name="19630" class="Keyword"
+ >where</a
+ ><a name="19635"
+ >
+ </a
+ ><a name="19638" href="StlcProp.html#19638" class="Function"
>Γ~Γ′</a
+ ><a name="19642"
+ > </a
+ ><a name="19643" class="Symbol"
+ >:</a
+ ><a name="19644"
+ > </a
+ ><a name="19645" class="Symbol"
+ >∀</a
+ ><a name="19646"
+ > </a
+ ><a name="19647" class="Symbol"
+ >{</a
+ ><a name="19648" href="StlcProp.html#19648" class="Bound"
+ >x</a
+ ><a name="19649" class="Symbol"
+ >}</a
+ ><a name="19650"
+ > </a
+ ><a name="19651" class="Symbol"
+ >→</a
+ ><a name="19652"
+ > </a
+ ><a name="19653" href="StlcProp.html#19648" class="Bound"
+ >x</a
+ ><a name="19654"
+ > </a
+ ><a name="19655" href="StlcProp.html#7659" class="Datatype Operator"
+ >∈</a
+ ><a name="19656"
+ > </a
+ ><a name="19657" href="StlcProp.html#19590" class="Bound"
+ >V</a
+ ><a name="19658"
+ > </a
+ ><a name="19659" class="Symbol"
+ >→</a
+ ><a name="19660"
+ > </a
+ ><a name="19661" href="Maps.html#10265" class="Function"
+ >∅</a
+ ><a name="19662"
+ > </a
+ ><a name="19663" href="StlcProp.html#19648" class="Bound"
+ >x</a
+ ><a name="19664"
+ > </a
+ ><a name="19665" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#83" class="Datatype Operator"
+ >≡</a
+ ><a name="19666"
+ > </a
+ ><a name="19667" href="StlcProp.html#19598" class="Bound"
+ >Γ</a
><a name="19668"
> </a
- ><a name="19669" class="Symbol"
- >{</a
- ><a name="19670" href="StlcProp.html#19670" class="Bound"
+ ><a name="19669" href="StlcProp.html#19648" class="Bound"
>x</a
- ><a name="19671" class="Symbol"
+ ><a name="19670"
+ >
+ </a
+ ><a name="19673" href="StlcProp.html#19638" class="Function"
+ >Γ~Γ′</a
+ ><a name="19677"
+ > </a
+ ><a name="19678" class="Symbol"
+ >{</a
+ ><a name="19679" href="StlcProp.html#19679" class="Bound"
+ >x</a
+ ><a name="19680" class="Symbol"
>}</a
- ><a name="19672"
+ ><a name="19681"
> </a
- ><a name="19673" href="StlcProp.html#19673" class="Bound"
+ ><a name="19682" href="StlcProp.html#19682" class="Bound"
>x∈V</a
- ><a name="19676"
- > </a
- ><a name="19677" class="Symbol"
- >=</a
- ><a name="19678"
- > </a
- ><a name="19679" href="https://agda.github.io/agda-stdlib/Data.Empty.html#348" class="Function"
- >⊥-elim</a
><a name="19685"
> </a
><a name="19686" class="Symbol"
- >(</a
- ><a name="19687" href="StlcProp.html#19710" class="Function"
- >x∉V</a
- ><a name="19690"
+ >=</a
+ ><a name="19687"
> </a
- ><a name="19691" href="StlcProp.html#19673" class="Bound"
+ ><a name="19688" href="https://agda.github.io/agda-stdlib/Data.Empty.html#348" class="Function"
+ >⊥-elim</a
+ ><a name="19694"
+ > </a
+ ><a name="19695" class="Symbol"
+ >(</a
+ ><a name="19696" href="StlcProp.html#19719" class="Function"
+ >x∉V</a
+ ><a name="19699"
+ > </a
+ ><a name="19700" href="StlcProp.html#19682" class="Bound"
>x∈V</a
- ><a name="19694" class="Symbol"
+ ><a name="19703" class="Symbol"
>)</a
- ><a name="19695"
+ ><a name="19704"
>
</a
- ><a name="19700" class="Keyword"
+ ><a name="19709" class="Keyword"
>where</a
- ><a name="19705"
+ ><a name="19714"
>
</a
- ><a name="19710" href="StlcProp.html#19710" class="Function"
+ ><a name="19719" href="StlcProp.html#19719" class="Function"
>x∉V</a
- ><a name="19713"
- > </a
- ><a name="19714" class="Symbol"
- >:</a
- ><a name="19715"
- > </a
- ><a name="19716" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#414" class="Function Operator"
- >¬</a
- ><a name="19717"
- > </a
- ><a name="19718" class="Symbol"
- >(</a
- ><a name="19719" href="StlcProp.html#19670" class="Bound"
- >x</a
- ><a name="19720"
- > </a
- ><a name="19721" href="StlcProp.html#7659" class="Datatype Operator"
- >∈</a
><a name="19722"
> </a
- ><a name="19723" href="StlcProp.html#19581" class="Bound"
+ ><a name="19723" class="Symbol"
+ >:</a
+ ><a name="19724"
+ > </a
+ ><a name="19725" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#414" class="Function Operator"
+ >¬</a
+ ><a name="19726"
+ > </a
+ ><a name="19727" class="Symbol"
+ >(</a
+ ><a name="19728" href="StlcProp.html#19679" class="Bound"
+ >x</a
+ ><a name="19729"
+ > </a
+ ><a name="19730" href="StlcProp.html#7659" class="Datatype Operator"
+ >∈</a
+ ><a name="19731"
+ > </a
+ ><a name="19732" href="StlcProp.html#19590" class="Bound"
>V</a
- ><a name="19724" class="Symbol"
+ ><a name="19733" class="Symbol"
>)</a
- ><a name="19725"
+ ><a name="19734"
>
</a
- ><a name="19730" href="StlcProp.html#19710" class="Function"
+ ><a name="19739" href="StlcProp.html#19719" class="Function"
>x∉V</a
- ><a name="19733"
+ ><a name="19742"
> </a
- ><a name="19734" class="Symbol"
+ ><a name="19743" class="Symbol"
>=</a
- ><a name="19735"
+ ><a name="19744"
> </a
- ><a name="19736" href="StlcProp.html#11791" class="Postulate"
+ ><a name="19745" href="StlcProp.html#11797" class="Postulate"
>∅⊢-closed</a
- ><a name="19745"
+ ><a name="19754"
> </a
- ><a name="19746" href="StlcProp.html#19592" class="Bound"
+ ><a name="19755" href="StlcProp.html#19601" class="Bound"
>⊢V</a
- ><a name="19748"
+ ><a name="19757"
> </a
- ><a name="19749" class="Symbol"
+ ><a name="19758" class="Symbol"
>{</a
- ><a name="19750" href="StlcProp.html#19670" class="Bound"
+ ><a name="19759" href="StlcProp.html#19679" class="Bound"
>x</a
- ><a name="19751" class="Symbol"
+ ><a name="19760" class="Symbol"
>}</a
- ><a name="19752"
+ ><a name="19761"
>
</a
- ><a name="19754" href="StlcProp.html#19754" class="Function"
+ ><a name="19763" href="StlcProp.html#19763" class="Function"
>just-injective</a
- ><a name="19768"
- > </a
- ><a name="19769" class="Symbol"
- >:</a
- ><a name="19770"
- > </a
- ><a name="19771" class="Symbol"
- >∀</a
- ><a name="19772"
- > </a
- ><a name="19773" class="Symbol"
- >{</a
- ><a name="19774" href="StlcProp.html#19774" class="Bound"
- >X</a
- ><a name="19775"
- > </a
- ><a name="19776" class="Symbol"
- >:</a
><a name="19777"
> </a
- ><a name="19778" class="PrimitiveType"
- >Set</a
- ><a name="19781" class="Symbol"
- >}</a
- ><a name="19782"
- > </a
- ><a name="19783" class="Symbol"
- >{</a
- ><a name="19784" href="StlcProp.html#19784" class="Bound"
- >x</a
- ><a name="19785"
- > </a
- ><a name="19786" href="StlcProp.html#19786" class="Bound"
- >y</a
- ><a name="19787"
- > </a
- ><a name="19788" class="Symbol"
+ ><a name="19778" class="Symbol"
>:</a
- ><a name="19789"
+ ><a name="19779"
> </a
- ><a name="19790" href="StlcProp.html#19774" class="Bound"
+ ><a name="19780" class="Symbol"
+ >∀</a
+ ><a name="19781"
+ > </a
+ ><a name="19782" class="Symbol"
+ >{</a
+ ><a name="19783" href="StlcProp.html#19783" class="Bound"
>X</a
- ><a name="19791" class="Symbol"
- >}</a
- ><a name="19792"
+ ><a name="19784"
> </a
- ><a name="19793" class="Symbol"
- >→</a
+ ><a name="19785" class="Symbol"
+ >:</a
+ ><a name="19786"
+ > </a
+ ><a name="19787" class="PrimitiveType"
+ >Set</a
+ ><a name="19790" class="Symbol"
+ >}</a
+ ><a name="19791"
+ > </a
+ ><a name="19792" class="Symbol"
+ >{</a
+ ><a name="19793" href="StlcProp.html#19793" class="Bound"
+ >x</a
><a name="19794"
> </a
- ><a name="19795" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#83" class="Datatype Operator"
- >_≡_</a
+ ><a name="19795" href="StlcProp.html#19795" class="Bound"
+ >y</a
+ ><a name="19796"
+ > </a
+ ><a name="19797" class="Symbol"
+ >:</a
><a name="19798"
> </a
- ><a name="19799" class="Symbol"
- >{</a
- ><a name="19800" class="Argument"
- >A</a
+ ><a name="19799" href="StlcProp.html#19783" class="Bound"
+ >X</a
+ ><a name="19800" class="Symbol"
+ >}</a
><a name="19801"
> </a
><a name="19802" class="Symbol"
- >=</a
+ >→</a
><a name="19803"
> </a
- ><a name="19804" href="https://agda.github.io/agda-stdlib/Data.Maybe.Base.html#335" class="Datatype"
- >Maybe</a
- ><a name="19809"
+ ><a name="19804" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#83" class="Datatype Operator"
+ >_≡_</a
+ ><a name="19807"
+ > </a
+ ><a name="19808" class="Symbol"
+ >{</a
+ ><a name="19809" class="Argument"
+ >A</a
+ ><a name="19810"
> </a
- ><a name="19810" href="StlcProp.html#19774" class="Bound"
- >X</a
><a name="19811" class="Symbol"
- >}</a
+ >=</a
><a name="19812"
> </a
- ><a name="19813" class="Symbol"
- >(</a
- ><a name="19814" href="https://agda.github.io/agda-stdlib/Data.Maybe.Base.html#373" class="InductiveConstructor"
- >just</a
+ ><a name="19813" href="https://agda.github.io/agda-stdlib/Data.Maybe.Base.html#335" class="Datatype"
+ >Maybe</a
><a name="19818"
> </a
- ><a name="19819" href="StlcProp.html#19784" class="Bound"
- >x</a
+ ><a name="19819" href="StlcProp.html#19783" class="Bound"
+ >X</a
><a name="19820" class="Symbol"
- >)</a
+ >}</a
><a name="19821"
> </a
><a name="19822" class="Symbol"
@@ -5421,42 +5409,54 @@ We need a couple of lemmas. A closed term can be weakened to any context, and `j
>just</a
><a name="19827"
> </a
- ><a name="19828" href="StlcProp.html#19786" class="Bound"
- >y</a
+ ><a name="19828" href="StlcProp.html#19793" class="Bound"
+ >x</a
><a name="19829" class="Symbol"
>)</a
><a name="19830"
> </a
><a name="19831" class="Symbol"
- >→</a
- ><a name="19832"
- > </a
- ><a name="19833" href="StlcProp.html#19784" class="Bound"
- >x</a
- ><a name="19834"
- > </a
- ><a name="19835" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#83" class="Datatype Operator"
- >≡</a
+ >(</a
+ ><a name="19832" href="https://agda.github.io/agda-stdlib/Data.Maybe.Base.html#373" class="InductiveConstructor"
+ >just</a
><a name="19836"
> </a
- ><a name="19837" href="StlcProp.html#19786" class="Bound"
+ ><a name="19837" href="StlcProp.html#19795" class="Bound"
>y</a
- ><a name="19838"
+ ><a name="19838" class="Symbol"
+ >)</a
+ ><a name="19839"
+ > </a
+ ><a name="19840" class="Symbol"
+ >→</a
+ ><a name="19841"
+ > </a
+ ><a name="19842" href="StlcProp.html#19793" class="Bound"
+ >x</a
+ ><a name="19843"
+ > </a
+ ><a name="19844" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#83" class="Datatype Operator"
+ >≡</a
+ ><a name="19845"
+ > </a
+ ><a name="19846" href="StlcProp.html#19795" class="Bound"
+ >y</a
+ ><a name="19847"
>
</a
- ><a name="19839" href="StlcProp.html#19754" class="Function"
+ ><a name="19848" href="StlcProp.html#19763" class="Function"
>just-injective</a
- ><a name="19853"
+ ><a name="19862"
> </a
- ><a name="19854" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#140" class="InductiveConstructor"
+ ><a name="19863" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#140" class="InductiveConstructor"
>refl</a
- ><a name="19858"
+ ><a name="19867"
> </a
- ><a name="19859" class="Symbol"
+ ><a name="19868" class="Symbol"
>=</a
- ><a name="19860"
+ ><a name="19869"
> </a
- ><a name="19861" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#140" class="InductiveConstructor"
+ ><a name="19870" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#140" class="InductiveConstructor"
>refl</a
>
@@ -5464,937 +5464,937 @@ We need a couple of lemmas. A closed term can be weakened to any context, and `j
<pre class="Agda">
-<a name="19891" href="StlcProp.html#16218" class="Function"
+<a name="19900" href="StlcProp.html#16224" class="Function"
>preservation-[:=]</a
- ><a name="19908"
+ ><a name="19917"
> </a
- ><a name="19909" class="Symbol"
+ ><a name="19918" class="Symbol"
>{</a
- ><a name="19910" href="StlcProp.html#19910" class="Bound"
+ ><a name="19919" href="StlcProp.html#19919" class="Bound"
>Γ</a
- ><a name="19911" class="Symbol"
+ ><a name="19920" class="Symbol"
>}</a
- ><a name="19912"
+ ><a name="19921"
> </a
- ><a name="19913" class="Symbol"
+ ><a name="19922" class="Symbol"
>{</a
- ><a name="19914" href="StlcProp.html#19914" class="Bound"
+ ><a name="19923" href="StlcProp.html#19923" class="Bound"
>x</a
- ><a name="19915" class="Symbol"
+ ><a name="19924" class="Symbol"
>}</a
- ><a name="19916"
+ ><a name="19925"
> </a
- ><a name="19917" class="Symbol"
+ ><a name="19926" class="Symbol"
>{</a
- ><a name="19918" href="StlcProp.html#19918" class="Bound"
+ ><a name="19927" href="StlcProp.html#19927" class="Bound"
>A</a
- ><a name="19919" class="Symbol"
+ ><a name="19928" class="Symbol"
>}</a
- ><a name="19920"
+ ><a name="19929"
> </a
- ><a name="19921" class="Symbol"
+ ><a name="19930" class="Symbol"
>(</a
- ><a name="19922" href="Stlc.html#3156" class="InductiveConstructor"
+ ><a name="19931" href="Stlc.html#6114" class="InductiveConstructor"
>Ax</a
- ><a name="19924"
+ ><a name="19933"
> </a
- ><a name="19925" class="Symbol"
+ ><a name="19934" class="Symbol"
>{</a
- ><a name="19926" href="StlcProp.html#19926" class="Bound"
+ ><a name="19935" href="StlcProp.html#19935" class="Bound"
>Γ,x∶A</a
- ><a name="19931" class="Symbol"
- >}</a
- ><a name="19932"
- > </a
- ><a name="19933" class="Symbol"
- >{</a
- ><a name="19934" href="StlcProp.html#19934" class="Bound"
- >x′</a
- ><a name="19936" class="Symbol"
- >}</a
- ><a name="19937"
- > </a
- ><a name="19938" class="Symbol"
- >{</a
- ><a name="19939" href="StlcProp.html#19939" class="Bound"
- >B</a
><a name="19940" class="Symbol"
>}</a
><a name="19941"
> </a
- ><a name="19942" href="StlcProp.html#19942" class="Bound"
+ ><a name="19942" class="Symbol"
+ >{</a
+ ><a name="19943" href="StlcProp.html#19943" class="Bound"
+ >x′</a
+ ><a name="19945" class="Symbol"
+ >}</a
+ ><a name="19946"
+ > </a
+ ><a name="19947" class="Symbol"
+ >{</a
+ ><a name="19948" href="StlcProp.html#19948" class="Bound"
+ >B</a
+ ><a name="19949" class="Symbol"
+ >}</a
+ ><a name="19950"
+ > </a
+ ><a name="19951" href="StlcProp.html#19951" class="Bound"
>[Γ,x∶A]x′≡B</a
- ><a name="19953" class="Symbol"
+ ><a name="19962" class="Symbol"
>)</a
- ><a name="19954"
+ ><a name="19963"
> </a
- ><a name="19955" href="StlcProp.html#19955" class="Bound"
+ ><a name="19964" href="StlcProp.html#19964" class="Bound"
>⊢V</a
- ><a name="19957"
- > </a
- ><a name="19958" class="Keyword"
- >with</a
- ><a name="19962"
- > </a
- ><a name="19963" href="StlcProp.html#19914" class="Bound"
- >x</a
- ><a name="19964"
- > </a
- ><a name="19965" href="Maps.html#2509" class="Function Operator"
- >≟</a
><a name="19966"
> </a
- ><a name="19967" href="StlcProp.html#19934" class="Bound"
+ ><a name="19967" class="Keyword"
+ >with</a
+ ><a name="19971"
+ > </a
+ ><a name="19972" href="StlcProp.html#19923" class="Bound"
+ >x</a
+ ><a name="19973"
+ > </a
+ ><a name="19974" href="Maps.html#2509" class="Function Operator"
+ >≟</a
+ ><a name="19975"
+ > </a
+ ><a name="19976" href="StlcProp.html#19943" class="Bound"
>x′</a
- ><a name="19969"
+ ><a name="19978"
>
</a
- ><a name="19970" class="Symbol"
+ ><a name="19979" class="Symbol"
>...|</a
- ><a name="19974"
- > </a
- ><a name="19975" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#520" class="InductiveConstructor"
- >yes</a
- ><a name="19978"
- > </a
- ><a name="19979" href="StlcProp.html#19979" class="Bound"
- >x≡x′</a
><a name="19983"
> </a
- ><a name="19984" class="Keyword"
+ ><a name="19984" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#520" class="InductiveConstructor"
+ >yes</a
+ ><a name="19987"
+ > </a
+ ><a name="19988" href="StlcProp.html#19988" class="Bound"
+ >x≡x′</a
+ ><a name="19992"
+ > </a
+ ><a name="19993" class="Keyword"
>rewrite</a
- ><a name="19991"
+ ><a name="20000"
> </a
- ><a name="19992" href="StlcProp.html#19754" class="Function"
+ ><a name="20001" href="StlcProp.html#19763" class="Function"
>just-injective</a
- ><a name="20006"
+ ><a name="20015"
> </a
- ><a name="20007" href="StlcProp.html#19942" class="Bound"
+ ><a name="20016" href="StlcProp.html#19951" class="Bound"
>[Γ,x∶A]x′≡B</a
- ><a name="20018"
+ ><a name="20027"
> </a
- ><a name="20020" class="Symbol"
+ ><a name="20029" class="Symbol"
>=</a
- ><a name="20021"
+ ><a name="20030"
> </a
- ><a name="20023" href="StlcProp.html#19516" class="Function"
+ ><a name="20032" href="StlcProp.html#19525" class="Function"
>weaken-closed</a
- ><a name="20036"
+ ><a name="20045"
> </a
- ><a name="20037" href="StlcProp.html#19955" class="Bound"
+ ><a name="20046" href="StlcProp.html#19964" class="Bound"
>⊢V</a
- ><a name="20039"
+ ><a name="20048"
>
</a
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</a
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> </a
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> </a
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</a
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- ><a name="20712" href="Stlc.html#3365" class="InductiveConstructor"
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> </a
- ><a name="20722" href="Stlc.html#3365" class="InductiveConstructor"
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</a
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</a
- ><a name="20760" href="StlcProp.html#16218" class="Function"
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+ ><a name="20801"
+ > </a
+ ><a name="20802" href="StlcProp.html#20802" class="Bound"
+ >⊢V</a
+ ><a name="20804"
+ > </a
+ ><a name="20805" class="Symbol"
+ >=</a
+ ><a name="20806"
>
</a
- ><a name="20800" href="Stlc.html#3434" class="InductiveConstructor"
+ ><a name="20809" href="Stlc.html#6392" class="InductiveConstructor"
>𝔹-E</a
- ><a name="20803"
+ ><a name="20812"
> </a
- ><a name="20804" class="Symbol"
+ ><a name="20813" class="Symbol"
>(</a
- ><a name="20805" href="StlcProp.html#16218" class="Function"
+ ><a name="20814" href="StlcProp.html#16224" class="Function"
>preservation-[:=]</a
- ><a name="20822"
+ ><a name="20831"
> </a
- ><a name="20823" href="StlcProp.html#20783" class="Bound"
+ ><a name="20832" href="StlcProp.html#20792" class="Bound"
>⊢L</a
- ><a name="20825"
+ ><a name="20834"
> </a
- ><a name="20826" href="StlcProp.html#20793" class="Bound"
+ ><a name="20835" href="StlcProp.html#20802" class="Bound"
>⊢V</a
- ><a name="20828" class="Symbol"
+ ><a name="20837" class="Symbol"
>)</a
- ><a name="20829"
+ ><a name="20838"
> </a
- ><a name="20830" class="Symbol"
+ ><a name="20839" class="Symbol"
>(</a
- ><a name="20831" href="StlcProp.html#16218" class="Function"
+ ><a name="20840" href="StlcProp.html#16224" class="Function"
>preservation-[:=]</a
- ><a name="20848"
+ ><a name="20857"
> </a
- ><a name="20849" href="StlcProp.html#20786" class="Bound"
+ ><a name="20858" href="StlcProp.html#20795" class="Bound"
>⊢M</a
- ><a name="20851"
+ ><a name="20860"
> </a
- ><a name="20852" href="StlcProp.html#20793" class="Bound"
+ ><a name="20861" href="StlcProp.html#20802" class="Bound"
>⊢V</a
- ><a name="20854" class="Symbol"
+ ><a name="20863" class="Symbol"
>)</a
- ><a name="20855"
+ ><a name="20864"
> </a
- ><a name="20856" class="Symbol"
+ ><a name="20865" class="Symbol"
>(</a
- ><a name="20857" href="StlcProp.html#16218" class="Function"
+ ><a name="20866" href="StlcProp.html#16224" class="Function"
>preservation-[:=]</a
- ><a name="20874"
+ ><a name="20883"
> </a
- ><a name="20875" href="StlcProp.html#20789" class="Bound"
+ ><a name="20884" href="StlcProp.html#20798" class="Bound"
>⊢N</a
- ><a name="20877"
+ ><a name="20886"
> </a
- ><a name="20878" href="StlcProp.html#20793" class="Bound"
+ ><a name="20887" href="StlcProp.html#20802" class="Bound"
>⊢V</a
- ><a name="20880" class="Symbol"
+ ><a name="20889" class="Symbol"
>)</a
>
@@ -6410,95 +6410,95 @@ reduction preserves types.
<pre class="Agda">
-<a name="21140" href="StlcProp.html#21140" class="Function"
+<a name="21149" href="StlcProp.html#21149" class="Function"
>preservation</a
- ><a name="21152"
- > </a
- ><a name="21153" class="Symbol"
- >:</a
- ><a name="21154"
- > </a
- ><a name="21155" class="Symbol"
- >∀</a
- ><a name="21156"
- > </a
- ><a name="21157" class="Symbol"
- >{</a
- ><a name="21158" href="StlcProp.html#21158" class="Bound"
- >M</a
- ><a name="21159"
- > </a
- ><a name="21160" href="StlcProp.html#21160" class="Bound"
- >N</a
><a name="21161"
> </a
- ><a name="21162" href="StlcProp.html#21162" class="Bound"
- >A</a
- ><a name="21163" class="Symbol"
- >}</a
- ><a name="21164"
+ ><a name="21162" class="Symbol"
+ >:</a
+ ><a name="21163"
> </a
- ><a name="21165" class="Symbol"
- >→</a
- ><a name="21166"
+ ><a name="21164" class="Symbol"
+ >∀</a
+ ><a name="21165"
> </a
- ><a name="21167" href="Maps.html#10265" class="Function"
- >∅</a
+ ><a name="21166" class="Symbol"
+ >{</a
+ ><a name="21167" href="StlcProp.html#21167" class="Bound"
+ >M</a
><a name="21168"
> </a
- ><a name="21169" href="Stlc.html#3112" class="Datatype Operator"
- >⊢</a
+ ><a name="21169" href="StlcProp.html#21169" class="Bound"
+ >N</a
><a name="21170"
> </a
- ><a name="21171" href="StlcProp.html#21158" class="Bound"
- >M</a
- ><a name="21172"
- > </a
- ><a name="21173" href="Stlc.html#3112" class="Datatype Operator"
- >∶</a
- ><a name="21174"
- > </a
- ><a name="21175" href="StlcProp.html#21162" class="Bound"
+ ><a name="21171" href="StlcProp.html#21171" class="Bound"
>A</a
- ><a name="21176"
+ ><a name="21172" class="Symbol"
+ >}</a
+ ><a name="21173"
> </a
- ><a name="21177" class="Symbol"
+ ><a name="21174" class="Symbol"
>→</a
- ><a name="21178"
+ ><a name="21175"
> </a
- ><a name="21179" href="StlcProp.html#21158" class="Bound"
- >M</a
- ><a name="21180"
- > </a
- ><a name="21181" href="Stlc.html#1762" class="Datatype Operator"
- >⟹</a
- ><a name="21182"
- > </a
- ><a name="21183" href="StlcProp.html#21160" class="Bound"
- >N</a
- ><a name="21184"
- > </a
- ><a name="21185" class="Symbol"
- >→</a
- ><a name="21186"
- > </a
- ><a name="21187" href="Maps.html#10265" class="Function"
+ ><a name="21176" href="Maps.html#10265" class="Function"
>∅</a
- ><a name="21188"
+ ><a name="21177"
> </a
- ><a name="21189" href="Stlc.html#3112" class="Datatype Operator"
+ ><a name="21178" href="Stlc.html#6070" class="Datatype Operator"
>⊢</a
- ><a name="21190"
+ ><a name="21179"
> </a
- ><a name="21191" href="StlcProp.html#21160" class="Bound"
- >N</a
- ><a name="21192"
+ ><a name="21180" href="StlcProp.html#21167" class="Bound"
+ >M</a
+ ><a name="21181"
> </a
- ><a name="21193" href="Stlc.html#3112" class="Datatype Operator"
+ ><a name="21182" href="Stlc.html#6070" class="Datatype Operator"
>∶</a
- ><a name="21194"
+ ><a name="21183"
> </a
- ><a name="21195" href="StlcProp.html#21162" class="Bound"
+ ><a name="21184" href="StlcProp.html#21171" class="Bound"
+ >A</a
+ ><a name="21185"
+ > </a
+ ><a name="21186" class="Symbol"
+ >→</a
+ ><a name="21187"
+ > </a
+ ><a name="21188" href="StlcProp.html#21167" class="Bound"
+ >M</a
+ ><a name="21189"
+ > </a
+ ><a name="21190" href="Stlc.html#4720" class="Datatype Operator"
+ >⟹</a
+ ><a name="21191"
+ > </a
+ ><a name="21192" href="StlcProp.html#21169" class="Bound"
+ >N</a
+ ><a name="21193"
+ > </a
+ ><a name="21194" class="Symbol"
+ >→</a
+ ><a name="21195"
+ > </a
+ ><a name="21196" href="Maps.html#10265" class="Function"
+ >∅</a
+ ><a name="21197"
+ > </a
+ ><a name="21198" href="Stlc.html#6070" class="Datatype Operator"
+ >⊢</a
+ ><a name="21199"
+ > </a
+ ><a name="21200" href="StlcProp.html#21169" class="Bound"
+ >N</a
+ ><a name="21201"
+ > </a
+ ><a name="21202" href="Stlc.html#6070" class="Datatype Operator"
+ >∶</a
+ ><a name="21203"
+ > </a
+ ><a name="21204" href="StlcProp.html#21171" class="Bound"
>A</a
>
@@ -6536,435 +6536,435 @@ _Proof_: By induction on the derivation of `∅ ⊢ M ∶ A`.
<pre class="Agda">
-<a name="22453" href="StlcProp.html#21140" class="Function"
+<a name="22462" href="StlcProp.html#21149" class="Function"
>preservation</a
- ><a name="22465"
+ ><a name="22474"
> </a
- ><a name="22466" class="Symbol"
+ ><a name="22475" class="Symbol"
>(</a
- ><a name="22467" href="Stlc.html#3156" class="InductiveConstructor"
+ ><a name="22476" href="Stlc.html#6114" class="InductiveConstructor"
>Ax</a
- ><a name="22469"
- > </a
- ><a name="22470" href="StlcProp.html#22470" class="Bound"
- >Γx≡A</a
- ><a name="22474" class="Symbol"
- >)</a
- ><a name="22475"
- > </a
- ><a name="22476" class="Symbol"
- >()</a
><a name="22478"
+ > </a
+ ><a name="22479" href="StlcProp.html#22479" class="Bound"
+ >Γx≡A</a
+ ><a name="22483" class="Symbol"
+ >)</a
+ ><a name="22484"
+ > </a
+ ><a name="22485" class="Symbol"
+ >()</a
+ ><a name="22487"
>
</a
- ><a name="22479" href="StlcProp.html#21140" class="Function"
+ ><a name="22488" href="StlcProp.html#21149" class="Function"
>preservation</a
- ><a name="22491"
- > </a
- ><a name="22492" class="Symbol"
- >(</a
- ><a name="22493" href="Stlc.html#3210" class="InductiveConstructor"
- >⇒-I</a
- ><a name="22496"
- > </a
- ><a name="22497" href="StlcProp.html#22497" class="Bound"
- >⊢N</a
- ><a name="22499" class="Symbol"
- >)</a
><a name="22500"
> </a
><a name="22501" class="Symbol"
+ >(</a
+ ><a name="22502" href="Stlc.html#6168" class="InductiveConstructor"
+ >⇒-I</a
+ ><a name="22505"
+ > </a
+ ><a name="22506" href="StlcProp.html#22506" class="Bound"
+ >⊢N</a
+ ><a name="22508" class="Symbol"
+ >)</a
+ ><a name="22509"
+ > </a
+ ><a name="22510" class="Symbol"
>()</a
- ><a name="22503"
+ ><a name="22512"
>
</a
- ><a name="22504" href="StlcProp.html#21140" class="Function"
+ ><a name="22513" href="StlcProp.html#21149" class="Function"
>preservation</a
- ><a name="22516"
+ ><a name="22525"
> </a
- ><a name="22517" class="Symbol"
+ ><a name="22526" class="Symbol"
>(</a
- ><a name="22518" href="Stlc.html#3287" class="InductiveConstructor"
+ ><a name="22527" href="Stlc.html#6245" class="InductiveConstructor"
>⇒-E</a
- ><a name="22521"
- > </a
- ><a name="22522" class="Symbol"
- >(</a
- ><a name="22523" href="Stlc.html#3210" class="InductiveConstructor"
- >⇒-I</a
- ><a name="22526"
- > </a
- ><a name="22527" href="StlcProp.html#22527" class="Bound"
- >⊢N</a
- ><a name="22529" class="Symbol"
- >)</a
><a name="22530"
> </a
- ><a name="22531" href="StlcProp.html#22531" class="Bound"
- >⊢V</a
- ><a name="22533" class="Symbol"
- >)</a
- ><a name="22534"
- > </a
- ><a name="22535" class="Symbol"
+ ><a name="22531" class="Symbol"
>(</a
- ><a name="22536" href="Stlc.html#1794" class="InductiveConstructor"
- >βλ·</a
+ ><a name="22532" href="Stlc.html#6168" class="InductiveConstructor"
+ >⇒-I</a
+ ><a name="22535"
+ > </a
+ ><a name="22536" href="StlcProp.html#22536" class="Bound"
+ >⊢N</a
+ ><a name="22538" class="Symbol"
+ >)</a
><a name="22539"
> </a
><a name="22540" href="StlcProp.html#22540" class="Bound"
- >valueV</a
- ><a name="22546" class="Symbol"
- >)</a
- ><a name="22547"
- > </a
- ><a name="22548" class="Symbol"
- >=</a
- ><a name="22549"
- > </a
- ><a name="22550" href="StlcProp.html#16218" class="Function"
- >preservation-[:=]</a
- ><a name="22567"
- > </a
- ><a name="22568" href="StlcProp.html#22527" class="Bound"
- >⊢N</a
- ><a name="22570"
- > </a
- ><a name="22571" href="StlcProp.html#22531" class="Bound"
>⊢V</a
- ><a name="22573"
+ ><a name="22542" class="Symbol"
+ >)</a
+ ><a name="22543"
+ > </a
+ ><a name="22544" class="Symbol"
+ >(</a
+ ><a name="22545" href="Stlc.html#4752" class="InductiveConstructor"
+ >βλ·</a
+ ><a name="22548"
+ > </a
+ ><a name="22549" href="StlcProp.html#22549" class="Bound"
+ >valueV</a
+ ><a name="22555" class="Symbol"
+ >)</a
+ ><a name="22556"
+ > </a
+ ><a name="22557" class="Symbol"
+ >=</a
+ ><a name="22558"
+ > </a
+ ><a name="22559" href="StlcProp.html#16224" class="Function"
+ >preservation-[:=]</a
+ ><a name="22576"
+ > </a
+ ><a name="22577" href="StlcProp.html#22536" class="Bound"
+ >⊢N</a
+ ><a name="22579"
+ > </a
+ ><a name="22580" href="StlcProp.html#22540" class="Bound"
+ >⊢V</a
+ ><a name="22582"
>
</a
- ><a name="22574" href="StlcProp.html#21140" class="Function"
+ ><a name="22583" href="StlcProp.html#21149" class="Function"
>preservation</a
- ><a name="22586"
+ ><a name="22595"
> </a
- ><a name="22587" class="Symbol"
+ ><a name="22596" class="Symbol"
>(</a
- ><a name="22588" href="Stlc.html#3287" class="InductiveConstructor"
+ ><a name="22597" href="Stlc.html#6245" class="InductiveConstructor"
>⇒-E</a
- ><a name="22591"
+ ><a name="22600"
> </a
- ><a name="22592" href="StlcProp.html#22592" class="Bound"
+ ><a name="22601" href="StlcProp.html#22601" class="Bound"
>⊢L</a
- ><a name="22594"
- > </a
- ><a name="22595" href="StlcProp.html#22595" class="Bound"
- >⊢M</a
- ><a name="22597" class="Symbol"
- >)</a
- ><a name="22598"
- > </a
- ><a name="22599" class="Symbol"
- >(</a
- ><a name="22600" href="Stlc.html#1864" class="InductiveConstructor"
- >ξ·₁</a
><a name="22603"
> </a
><a name="22604" href="StlcProp.html#22604" class="Bound"
- >L⟹L′</a
+ >⊢M</a
+ ><a name="22606" class="Symbol"
+ >)</a
+ ><a name="22607"
+ > </a
><a name="22608" class="Symbol"
- >)</a
- ><a name="22609"
+ >(</a
+ ><a name="22609" href="Stlc.html#4822" class="InductiveConstructor"
+ >ξ·₁</a
+ ><a name="22612"
> </a
- ><a name="22610" class="Keyword"
- >with</a
- ><a name="22614"
- > </a
- ><a name="22615" href="StlcProp.html#21140" class="Function"
- >preservation</a
- ><a name="22627"
- > </a
- ><a name="22628" href="StlcProp.html#22592" class="Bound"
- >⊢L</a
- ><a name="22630"
- > </a
- ><a name="22631" href="StlcProp.html#22604" class="Bound"
+ ><a name="22613" href="StlcProp.html#22613" class="Bound"
>L⟹L′</a
- ><a name="22635"
- >
-</a
- ><a name="22636" class="Symbol"
- >...|</a
- ><a name="22640"
- > </a
- ><a name="22641" href="StlcProp.html#22641" class="Bound"
- >⊢L′</a
- ><a name="22644"
- > </a
- ><a name="22645" class="Symbol"
- >=</a
- ><a name="22646"
- > </a
- ><a name="22647" href="Stlc.html#3287" class="InductiveConstructor"
- >⇒-E</a
- ><a name="22650"
- > </a
- ><a name="22651" href="StlcProp.html#22641" class="Bound"
- >⊢L′</a
- ><a name="22654"
- > </a
- ><a name="22655" href="StlcProp.html#22595" class="Bound"
- >⊢M</a
- ><a name="22657"
- >
-</a
- ><a name="22658" href="StlcProp.html#21140" class="Function"
- >preservation</a
- ><a name="22670"
- > </a
- ><a name="22671" class="Symbol"
- >(</a
- ><a name="22672" href="Stlc.html#3287" class="InductiveConstructor"
- >⇒-E</a
- ><a name="22675"
- > </a
- ><a name="22676" href="StlcProp.html#22676" class="Bound"
- >⊢L</a
- ><a name="22678"
- > </a
- ><a name="22679" href="StlcProp.html#22679" class="Bound"
- >⊢M</a
- ><a name="22681" class="Symbol"
+ ><a name="22617" class="Symbol"
>)</a
- ><a name="22682"
+ ><a name="22618"
> </a
- ><a name="22683" class="Symbol"
+ ><a name="22619" class="Keyword"
+ >with</a
+ ><a name="22623"
+ > </a
+ ><a name="22624" href="StlcProp.html#21149" class="Function"
+ >preservation</a
+ ><a name="22636"
+ > </a
+ ><a name="22637" href="StlcProp.html#22601" class="Bound"
+ >⊢L</a
+ ><a name="22639"
+ > </a
+ ><a name="22640" href="StlcProp.html#22613" class="Bound"
+ >L⟹L′</a
+ ><a name="22644"
+ >
+</a
+ ><a name="22645" class="Symbol"
+ >...|</a
+ ><a name="22649"
+ > </a
+ ><a name="22650" href="StlcProp.html#22650" class="Bound"
+ >⊢L′</a
+ ><a name="22653"
+ > </a
+ ><a name="22654" class="Symbol"
+ >=</a
+ ><a name="22655"
+ > </a
+ ><a name="22656" href="Stlc.html#6245" class="InductiveConstructor"
+ >⇒-E</a
+ ><a name="22659"
+ > </a
+ ><a name="22660" href="StlcProp.html#22650" class="Bound"
+ >⊢L′</a
+ ><a name="22663"
+ > </a
+ ><a name="22664" href="StlcProp.html#22604" class="Bound"
+ >⊢M</a
+ ><a name="22666"
+ >
+</a
+ ><a name="22667" href="StlcProp.html#21149" class="Function"
+ >preservation</a
+ ><a name="22679"
+ > </a
+ ><a name="22680" class="Symbol"
>(</a
- ><a name="22684" href="Stlc.html#1917" class="InductiveConstructor"
- >ξ·₂</a
+ ><a name="22681" href="Stlc.html#6245" class="InductiveConstructor"
+ >⇒-E</a
+ ><a name="22684"
+ > </a
+ ><a name="22685" href="StlcProp.html#22685" class="Bound"
+ >⊢L</a
><a name="22687"
> </a
><a name="22688" href="StlcProp.html#22688" class="Bound"
- >valueL</a
- ><a name="22694"
- > </a
- ><a name="22695" href="StlcProp.html#22695" class="Bound"
- >M⟹M′</a
- ><a name="22699" class="Symbol"
- >)</a
- ><a name="22700"
- > </a
- ><a name="22701" class="Keyword"
- >with</a
- ><a name="22705"
- > </a
- ><a name="22706" href="StlcProp.html#21140" class="Function"
- >preservation</a
- ><a name="22718"
- > </a
- ><a name="22719" href="StlcProp.html#22679" class="Bound"
>⊢M</a
- ><a name="22721"
+ ><a name="22690" class="Symbol"
+ >)</a
+ ><a name="22691"
> </a
- ><a name="22722" href="StlcProp.html#22695" class="Bound"
+ ><a name="22692" class="Symbol"
+ >(</a
+ ><a name="22693" href="Stlc.html#4875" class="InductiveConstructor"
+ >ξ·₂</a
+ ><a name="22696"
+ > </a
+ ><a name="22697" href="StlcProp.html#22697" class="Bound"
+ >valueL</a
+ ><a name="22703"
+ > </a
+ ><a name="22704" href="StlcProp.html#22704" class="Bound"
>M⟹M′</a
- ><a name="22726"
+ ><a name="22708" class="Symbol"
+ >)</a
+ ><a name="22709"
+ > </a
+ ><a name="22710" class="Keyword"
+ >with</a
+ ><a name="22714"
+ > </a
+ ><a name="22715" href="StlcProp.html#21149" class="Function"
+ >preservation</a
+ ><a name="22727"
+ > </a
+ ><a name="22728" href="StlcProp.html#22688" class="Bound"
+ >⊢M</a
+ ><a name="22730"
+ > </a
+ ><a name="22731" href="StlcProp.html#22704" class="Bound"
+ >M⟹M′</a
+ ><a name="22735"
>
</a
- ><a name="22727" class="Symbol"
- >...|</a
- ><a name="22731"
- > </a
- ><a name="22732" href="StlcProp.html#22732" class="Bound"
- >⊢M′</a
- ><a name="22735"
- > </a
><a name="22736" class="Symbol"
- >=</a
- ><a name="22737"
+ >...|</a
+ ><a name="22740"
> </a
- ><a name="22738" href="Stlc.html#3287" class="InductiveConstructor"
- >⇒-E</a
- ><a name="22741"
- > </a
- ><a name="22742" href="StlcProp.html#22676" class="Bound"
- >⊢L</a
+ ><a name="22741" href="StlcProp.html#22741" class="Bound"
+ >⊢M′</a
><a name="22744"
> </a
- ><a name="22745" href="StlcProp.html#22732" class="Bound"
+ ><a name="22745" class="Symbol"
+ >=</a
+ ><a name="22746"
+ > </a
+ ><a name="22747" href="Stlc.html#6245" class="InductiveConstructor"
+ >⇒-E</a
+ ><a name="22750"
+ > </a
+ ><a name="22751" href="StlcProp.html#22685" class="Bound"
+ >⊢L</a
+ ><a name="22753"
+ > </a
+ ><a name="22754" href="StlcProp.html#22741" class="Bound"
>⊢M′</a
- ><a name="22748"
+ ><a name="22757"
>
</a
- ><a name="22749" href="StlcProp.html#21140" class="Function"
+ ><a name="22758" href="StlcProp.html#21149" class="Function"
>preservation</a
- ><a name="22761"
+ ><a name="22770"
> </a
- ><a name="22762" href="Stlc.html#3365" class="InductiveConstructor"
+ ><a name="22771" href="Stlc.html#6323" class="InductiveConstructor"
>𝔹-I₁</a
- ><a name="22766"
+ ><a name="22775"
> </a
- ><a name="22767" class="Symbol"
+ ><a name="22776" class="Symbol"
>()</a
- ><a name="22769"
+ ><a name="22778"
>
</a
- ><a name="22770" href="StlcProp.html#21140" class="Function"
+ ><a name="22779" href="StlcProp.html#21149" class="Function"
>preservation</a
- ><a name="22782"
+ ><a name="22791"
> </a
- ><a name="22783" href="Stlc.html#3399" class="InductiveConstructor"
+ ><a name="22792" href="Stlc.html#6357" class="InductiveConstructor"
>𝔹-I₂</a
- ><a name="22787"
+ ><a name="22796"
> </a
- ><a name="22788" class="Symbol"
+ ><a name="22797" class="Symbol"
>()</a
- ><a name="22790"
+ ><a name="22799"
>
</a
- ><a name="22791" href="StlcProp.html#21140" class="Function"
+ ><a name="22800" href="StlcProp.html#21149" class="Function"
>preservation</a
- ><a name="22803"
+ ><a name="22812"
> </a
- ><a name="22804" class="Symbol"
+ ><a name="22813" class="Symbol"
>(</a
- ><a name="22805" href="Stlc.html#3434" class="InductiveConstructor"
+ ><a name="22814" href="Stlc.html#6392" class="InductiveConstructor"
>𝔹-E</a
- ><a name="22808"
+ ><a name="22817"
> </a
- ><a name="22809" href="Stlc.html#3365" class="InductiveConstructor"
+ ><a name="22818" href="Stlc.html#6323" class="InductiveConstructor"
>𝔹-I₁</a
- ><a name="22813"
+ ><a name="22822"
> </a
- ><a name="22814" href="StlcProp.html#22814" class="Bound"
+ ><a name="22823" href="StlcProp.html#22823" class="Bound"
>⊢M</a
- ><a name="22816"
+ ><a name="22825"
> </a
- ><a name="22817" href="StlcProp.html#22817" class="Bound"
+ ><a name="22826" href="StlcProp.html#22826" class="Bound"
>⊢N</a
- ><a name="22819" class="Symbol"
+ ><a name="22828" class="Symbol"
>)</a
- ><a name="22820"
- > </a
- ><a name="22821" href="Stlc.html#1984" class="InductiveConstructor"
- >βif-true</a
><a name="22829"
> </a
- ><a name="22830" class="Symbol"
- >=</a
- ><a name="22831"
+ ><a name="22830" href="Stlc.html#4942" class="InductiveConstructor"
+ >βif-true</a
+ ><a name="22838"
> </a
- ><a name="22832" href="StlcProp.html#22814" class="Bound"
+ ><a name="22839" class="Symbol"
+ >=</a
+ ><a name="22840"
+ > </a
+ ><a name="22841" href="StlcProp.html#22823" class="Bound"
>⊢M</a
- ><a name="22834"
+ ><a name="22843"
>
</a
- ><a name="22835" href="StlcProp.html#21140" class="Function"
+ ><a name="22844" href="StlcProp.html#21149" class="Function"
>preservation</a
- ><a name="22847"
+ ><a name="22856"
> </a
- ><a name="22848" class="Symbol"
+ ><a name="22857" class="Symbol"
>(</a
- ><a name="22849" href="Stlc.html#3434" class="InductiveConstructor"
+ ><a name="22858" href="Stlc.html#6392" class="InductiveConstructor"
>𝔹-E</a
- ><a name="22852"
+ ><a name="22861"
> </a
- ><a name="22853" href="Stlc.html#3399" class="InductiveConstructor"
+ ><a name="22862" href="Stlc.html#6357" class="InductiveConstructor"
>𝔹-I₂</a
- ><a name="22857"
+ ><a name="22866"
> </a
- ><a name="22858" href="StlcProp.html#22858" class="Bound"
+ ><a name="22867" href="StlcProp.html#22867" class="Bound"
>⊢M</a
- ><a name="22860"
+ ><a name="22869"
> </a
- ><a name="22861" href="StlcProp.html#22861" class="Bound"
+ ><a name="22870" href="StlcProp.html#22870" class="Bound"
>⊢N</a
- ><a name="22863" class="Symbol"
+ ><a name="22872" class="Symbol"
>)</a
- ><a name="22864"
+ ><a name="22873"
> </a
- ><a name="22865" href="Stlc.html#2037" class="InductiveConstructor"
+ ><a name="22874" href="Stlc.html#4995" class="InductiveConstructor"
>βif-false</a
- ><a name="22874"
+ ><a name="22883"
> </a
- ><a name="22875" class="Symbol"
+ ><a name="22884" class="Symbol"
>=</a
- ><a name="22876"
+ ><a name="22885"
> </a
- ><a name="22877" href="StlcProp.html#22861" class="Bound"
+ ><a name="22886" href="StlcProp.html#22870" class="Bound"
>⊢N</a
- ><a name="22879"
+ ><a name="22888"
>
</a
- ><a name="22880" href="StlcProp.html#21140" class="Function"
+ ><a name="22889" href="StlcProp.html#21149" class="Function"
>preservation</a
- ><a name="22892"
+ ><a name="22901"
> </a
- ><a name="22893" class="Symbol"
+ ><a name="22902" class="Symbol"
>(</a
- ><a name="22894" href="Stlc.html#3434" class="InductiveConstructor"
+ ><a name="22903" href="Stlc.html#6392" class="InductiveConstructor"
>𝔹-E</a
- ><a name="22897"
+ ><a name="22906"
> </a
- ><a name="22898" href="StlcProp.html#22898" class="Bound"
+ ><a name="22907" href="StlcProp.html#22907" class="Bound"
>⊢L</a
- ><a name="22900"
+ ><a name="22909"
> </a
- ><a name="22901" href="StlcProp.html#22901" class="Bound"
+ ><a name="22910" href="StlcProp.html#22910" class="Bound"
>⊢M</a
- ><a name="22903"
- > </a
- ><a name="22904" href="StlcProp.html#22904" class="Bound"
- >⊢N</a
- ><a name="22906" class="Symbol"
- >)</a
- ><a name="22907"
- > </a
- ><a name="22908" class="Symbol"
- >(</a
- ><a name="22909" href="Stlc.html#2092" class="InductiveConstructor"
- >ξif</a
><a name="22912"
> </a
><a name="22913" href="StlcProp.html#22913" class="Bound"
- >L⟹L′</a
- ><a name="22917" class="Symbol"
+ >⊢N</a
+ ><a name="22915" class="Symbol"
>)</a
- ><a name="22918"
+ ><a name="22916"
> </a
- ><a name="22919" class="Keyword"
- >with</a
- ><a name="22923"
+ ><a name="22917" class="Symbol"
+ >(</a
+ ><a name="22918" href="Stlc.html#5050" class="InductiveConstructor"
+ >ξif</a
+ ><a name="22921"
> </a
- ><a name="22924" href="StlcProp.html#21140" class="Function"
- >preservation</a
- ><a name="22936"
- > </a
- ><a name="22937" href="StlcProp.html#22898" class="Bound"
- >⊢L</a
- ><a name="22939"
- > </a
- ><a name="22940" href="StlcProp.html#22913" class="Bound"
+ ><a name="22922" href="StlcProp.html#22922" class="Bound"
>L⟹L′</a
- ><a name="22944"
+ ><a name="22926" class="Symbol"
+ >)</a
+ ><a name="22927"
+ > </a
+ ><a name="22928" class="Keyword"
+ >with</a
+ ><a name="22932"
+ > </a
+ ><a name="22933" href="StlcProp.html#21149" class="Function"
+ >preservation</a
+ ><a name="22945"
+ > </a
+ ><a name="22946" href="StlcProp.html#22907" class="Bound"
+ >⊢L</a
+ ><a name="22948"
+ > </a
+ ><a name="22949" href="StlcProp.html#22922" class="Bound"
+ >L⟹L′</a
+ ><a name="22953"
>
</a
- ><a name="22945" class="Symbol"
- >...|</a
- ><a name="22949"
- > </a
- ><a name="22950" href="StlcProp.html#22950" class="Bound"
- >⊢L′</a
- ><a name="22953"
- > </a
><a name="22954" class="Symbol"
- >=</a
- ><a name="22955"
+ >...|</a
+ ><a name="22958"
> </a
- ><a name="22956" href="Stlc.html#3434" class="InductiveConstructor"
- >𝔹-E</a
- ><a name="22959"
- > </a
- ><a name="22960" href="StlcProp.html#22950" class="Bound"
+ ><a name="22959" href="StlcProp.html#22959" class="Bound"
>⊢L′</a
- ><a name="22963"
+ ><a name="22962"
> </a
- ><a name="22964" href="StlcProp.html#22901" class="Bound"
+ ><a name="22963" class="Symbol"
+ >=</a
+ ><a name="22964"
+ > </a
+ ><a name="22965" href="Stlc.html#6392" class="InductiveConstructor"
+ >𝔹-E</a
+ ><a name="22968"
+ > </a
+ ><a name="22969" href="StlcProp.html#22959" class="Bound"
+ >⊢L′</a
+ ><a name="22972"
+ > </a
+ ><a name="22973" href="StlcProp.html#22910" class="Bound"
>⊢M</a
- ><a name="22966"
+ ><a name="22975"
> </a
- ><a name="22967" href="StlcProp.html#22904" class="Bound"
+ ><a name="22976" href="StlcProp.html#22913" class="Bound"
>⊢N</a
>
@@ -6988,226 +6988,226 @@ term can _never_ reach a stuck state.
<pre class="Agda">
-<a name="23620" href="StlcProp.html#23620" class="Function"
+<a name="23629" href="StlcProp.html#23629" class="Function"
>Normal</a
- ><a name="23626"
- > </a
- ><a name="23627" class="Symbol"
- >:</a
- ><a name="23628"
- > </a
- ><a name="23629" href="Stlc.html#708" class="Datatype"
- >Term</a
- ><a name="23633"
- > </a
- ><a name="23634" class="Symbol"
- >→</a
><a name="23635"
> </a
- ><a name="23636" class="PrimitiveType"
+ ><a name="23636" class="Symbol"
+ >:</a
+ ><a name="23637"
+ > </a
+ ><a name="23638" href="Stlc.html#3485" class="Datatype"
+ >Term</a
+ ><a name="23642"
+ > </a
+ ><a name="23643" class="Symbol"
+ >→</a
+ ><a name="23644"
+ > </a
+ ><a name="23645" class="PrimitiveType"
>Set</a
- ><a name="23639"
+ ><a name="23648"
>
</a
- ><a name="23640" href="StlcProp.html#23620" class="Function"
+ ><a name="23649" href="StlcProp.html#23629" class="Function"
>Normal</a
- ><a name="23646"
+ ><a name="23655"
> </a
- ><a name="23647" href="StlcProp.html#23647" class="Bound"
+ ><a name="23656" href="StlcProp.html#23656" class="Bound"
>M</a
- ><a name="23648"
+ ><a name="23657"
> </a
- ><a name="23649" class="Symbol"
+ ><a name="23658" class="Symbol"
>=</a
- ><a name="23650"
+ ><a name="23659"
> </a
- ><a name="23651" class="Symbol"
+ ><a name="23660" class="Symbol"
>∀</a
- ><a name="23652"
+ ><a name="23661"
> </a
- ><a name="23653" class="Symbol"
+ ><a name="23662" class="Symbol"
>{</a
- ><a name="23654" href="StlcProp.html#23654" class="Bound"
+ ><a name="23663" href="StlcProp.html#23663" class="Bound"
>N</a
- ><a name="23655" class="Symbol"
+ ><a name="23664" class="Symbol"
>}</a
- ><a name="23656"
- > </a
- ><a name="23657" class="Symbol"
- >→</a
- ><a name="23658"
- > </a
- ><a name="23659" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#414" class="Function Operator"
- >¬</a
- ><a name="23660"
- > </a
- ><a name="23661" class="Symbol"
- >(</a
- ><a name="23662" href="StlcProp.html#23647" class="Bound"
- >M</a
- ><a name="23663"
- > </a
- ><a name="23664" href="Stlc.html#1762" class="Datatype Operator"
- >⟹</a
><a name="23665"
> </a
- ><a name="23666" href="StlcProp.html#23654" class="Bound"
+ ><a name="23666" class="Symbol"
+ >→</a
+ ><a name="23667"
+ > </a
+ ><a name="23668" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#414" class="Function Operator"
+ >¬</a
+ ><a name="23669"
+ > </a
+ ><a name="23670" class="Symbol"
+ >(</a
+ ><a name="23671" href="StlcProp.html#23656" class="Bound"
+ >M</a
+ ><a name="23672"
+ > </a
+ ><a name="23673" href="Stlc.html#4720" class="Datatype Operator"
+ >⟹</a
+ ><a name="23674"
+ > </a
+ ><a name="23675" href="StlcProp.html#23663" class="Bound"
>N</a
- ><a name="23667" class="Symbol"
+ ><a name="23676" class="Symbol"
>)</a
- ><a name="23668"
+ ><a name="23677"
>
</a
- ><a name="23670" href="StlcProp.html#23670" class="Function"
+ ><a name="23679" href="StlcProp.html#23679" class="Function"
>Stuck</a
- ><a name="23675"
- > </a
- ><a name="23676" class="Symbol"
- >:</a
- ><a name="23677"
- > </a
- ><a name="23678" href="Stlc.html#708" class="Datatype"
- >Term</a
- ><a name="23682"
- > </a
- ><a name="23683" class="Symbol"
- >→</a
><a name="23684"
> </a
- ><a name="23685" class="PrimitiveType"
+ ><a name="23685" class="Symbol"
+ >:</a
+ ><a name="23686"
+ > </a
+ ><a name="23687" href="Stlc.html#3485" class="Datatype"
+ >Term</a
+ ><a name="23691"
+ > </a
+ ><a name="23692" class="Symbol"
+ >→</a
+ ><a name="23693"
+ > </a
+ ><a name="23694" class="PrimitiveType"
>Set</a
- ><a name="23688"
+ ><a name="23697"
>
</a
- ><a name="23689" href="StlcProp.html#23670" class="Function"
+ ><a name="23698" href="StlcProp.html#23679" class="Function"
>Stuck</a
- ><a name="23694"
+ ><a name="23703"
> </a
- ><a name="23695" href="StlcProp.html#23695" class="Bound"
+ ><a name="23704" href="StlcProp.html#23704" class="Bound"
>M</a
- ><a name="23696"
- > </a
- ><a name="23697" class="Symbol"
- >=</a
- ><a name="23698"
- > </a
- ><a name="23699" href="StlcProp.html#23620" class="Function"
- >Normal</a
><a name="23705"
> </a
- ><a name="23706" href="StlcProp.html#23695" class="Bound"
- >M</a
+ ><a name="23706" class="Symbol"
+ >=</a
><a name="23707"
> </a
- ><a name="23708" href="https://agda.github.io/agda-stdlib/Data.Product.html#1073" class="Function Operator"
- >×</a
- ><a name="23709"
+ ><a name="23708" href="StlcProp.html#23629" class="Function"
+ >Normal</a
+ ><a name="23714"
> </a
- ><a name="23710" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#414" class="Function Operator"
- >¬</a
- ><a name="23711"
- > </a
- ><a name="23712" href="Stlc.html#1105" class="Datatype"
- >Value</a
- ><a name="23717"
- > </a
- ><a name="23718" href="StlcProp.html#23695" class="Bound"
+ ><a name="23715" href="StlcProp.html#23704" class="Bound"
>M</a
- ><a name="23719"
+ ><a name="23716"
+ > </a
+ ><a name="23717" href="https://agda.github.io/agda-stdlib/Data.Product.html#1073" class="Function Operator"
+ >×</a
+ ><a name="23718"
+ > </a
+ ><a name="23719" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#414" class="Function Operator"
+ >¬</a
+ ><a name="23720"
+ > </a
+ ><a name="23721" href="Stlc.html#4063" class="Datatype"
+ >Value</a
+ ><a name="23726"
+ > </a
+ ><a name="23727" href="StlcProp.html#23704" class="Bound"
+ >M</a
+ ><a name="23728"
>
</a
- ><a name="23721" class="Keyword"
+ ><a name="23730" class="Keyword"
>postulate</a
- ><a name="23730"
+ ><a name="23739"
>
</a
- ><a name="23733" href="StlcProp.html#23733" class="Postulate"
+ ><a name="23742" href="StlcProp.html#23742" class="Postulate"
>Soundness</a
- ><a name="23742"
- > </a
- ><a name="23743" class="Symbol"
- >:</a
- ><a name="23744"
- > </a
- ><a name="23745" class="Symbol"
- >∀</a
- ><a name="23746"
- > </a
- ><a name="23747" class="Symbol"
- >{</a
- ><a name="23748" href="StlcProp.html#23748" class="Bound"
- >M</a
- ><a name="23749"
- > </a
- ><a name="23750" href="StlcProp.html#23750" class="Bound"
- >N</a
><a name="23751"
> </a
- ><a name="23752" href="StlcProp.html#23752" class="Bound"
- >A</a
- ><a name="23753" class="Symbol"
- >}</a
- ><a name="23754"
+ ><a name="23752" class="Symbol"
+ >:</a
+ ><a name="23753"
> </a
- ><a name="23755" class="Symbol"
- >→</a
- ><a name="23756"
+ ><a name="23754" class="Symbol"
+ >∀</a
+ ><a name="23755"
> </a
- ><a name="23757" href="Maps.html#10265" class="Function"
- >∅</a
+ ><a name="23756" class="Symbol"
+ >{</a
+ ><a name="23757" href="StlcProp.html#23757" class="Bound"
+ >M</a
><a name="23758"
> </a
- ><a name="23759" href="Stlc.html#3112" class="Datatype Operator"
- >⊢</a
+ ><a name="23759" href="StlcProp.html#23759" class="Bound"
+ >N</a
><a name="23760"
> </a
- ><a name="23761" href="StlcProp.html#23748" class="Bound"
- >M</a
- ><a name="23762"
- > </a
- ><a name="23763" href="Stlc.html#3112" class="Datatype Operator"
- >∶</a
- ><a name="23764"
- > </a
- ><a name="23765" href="StlcProp.html#23752" class="Bound"
+ ><a name="23761" href="StlcProp.html#23761" class="Bound"
>A</a
- ><a name="23766"
+ ><a name="23762" class="Symbol"
+ >}</a
+ ><a name="23763"
> </a
- ><a name="23767" class="Symbol"
+ ><a name="23764" class="Symbol"
>→</a
- ><a name="23768"
+ ><a name="23765"
> </a
- ><a name="23769" href="StlcProp.html#23748" class="Bound"
+ ><a name="23766" href="Maps.html#10265" class="Function"
+ >∅</a
+ ><a name="23767"
+ > </a
+ ><a name="23768" href="Stlc.html#6070" class="Datatype Operator"
+ >⊢</a
+ ><a name="23769"
+ > </a
+ ><a name="23770" href="StlcProp.html#23757" class="Bound"
>M</a
- ><a name="23770"
+ ><a name="23771"
> </a
- ><a name="23771" href="Stlc.html#2287" class="Datatype Operator"
- >⟹*</a
+ ><a name="23772" href="Stlc.html#6070" class="Datatype Operator"
+ >∶</a
><a name="23773"
> </a
- ><a name="23774" href="StlcProp.html#23750" class="Bound"
- >N</a
+ ><a name="23774" href="StlcProp.html#23761" class="Bound"
+ >A</a
><a name="23775"
> </a
><a name="23776" class="Symbol"
>→</a
><a name="23777"
> </a
- ><a name="23778" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#414" class="Function Operator"
- >¬</a
+ ><a name="23778" href="StlcProp.html#23757" class="Bound"
+ >M</a
><a name="23779"
> </a
- ><a name="23780" class="Symbol"
- >(</a
- ><a name="23781" href="StlcProp.html#23670" class="Function"
- >Stuck</a
+ ><a name="23780" href="Stlc.html#5245" class="Datatype Operator"
+ >⟹*</a
+ ><a name="23782"
+ > </a
+ ><a name="23783" href="StlcProp.html#23759" class="Bound"
+ >N</a
+ ><a name="23784"
+ > </a
+ ><a name="23785" class="Symbol"
+ >→</a
><a name="23786"
> </a
- ><a name="23787" href="StlcProp.html#23750" class="Bound"
+ ><a name="23787" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#414" class="Function Operator"
+ >¬</a
+ ><a name="23788"
+ > </a
+ ><a name="23789" class="Symbol"
+ >(</a
+ ><a name="23790" href="StlcProp.html#23679" class="Function"
+ >Stuck</a
+ ><a name="23795"
+ > </a
+ ><a name="23796" href="StlcProp.html#23759" class="Bound"
>N</a
- ><a name="23788" class="Symbol"
+ ><a name="23797" class="Symbol"
>)</a
>
@@ -7216,342 +7216,342 @@ term can _never_ reach a stuck state.
<div class="hidden">
<pre class="Agda">
-<a name="23836" href="StlcProp.html#23836" class="Function"
+<a name="23845" href="StlcProp.html#23845" class="Function"
>Soundness′</a
- ><a name="23846"
- > </a
- ><a name="23847" class="Symbol"
- >:</a
- ><a name="23848"
- > </a
- ><a name="23849" class="Symbol"
- >∀</a
- ><a name="23850"
- > </a
- ><a name="23851" class="Symbol"
- >{</a
- ><a name="23852" href="StlcProp.html#23852" class="Bound"
- >M</a
- ><a name="23853"
- > </a
- ><a name="23854" href="StlcProp.html#23854" class="Bound"
- >N</a
><a name="23855"
> </a
- ><a name="23856" href="StlcProp.html#23856" class="Bound"
- >A</a
- ><a name="23857" class="Symbol"
- >}</a
- ><a name="23858"
+ ><a name="23856" class="Symbol"
+ >:</a
+ ><a name="23857"
> </a
- ><a name="23859" class="Symbol"
- >→</a
- ><a name="23860"
+ ><a name="23858" class="Symbol"
+ >∀</a
+ ><a name="23859"
> </a
- ><a name="23861" href="Maps.html#10265" class="Function"
- >∅</a
+ ><a name="23860" class="Symbol"
+ >{</a
+ ><a name="23861" href="StlcProp.html#23861" class="Bound"
+ >M</a
><a name="23862"
> </a
- ><a name="23863" href="Stlc.html#3112" class="Datatype Operator"
- >⊢</a
+ ><a name="23863" href="StlcProp.html#23863" class="Bound"
+ >N</a
><a name="23864"
> </a
- ><a name="23865" href="StlcProp.html#23852" class="Bound"
- >M</a
- ><a name="23866"
- > </a
- ><a name="23867" href="Stlc.html#3112" class="Datatype Operator"
- >∶</a
- ><a name="23868"
- > </a
- ><a name="23869" href="StlcProp.html#23856" class="Bound"
+ ><a name="23865" href="StlcProp.html#23865" class="Bound"
>A</a
- ><a name="23870"
+ ><a name="23866" class="Symbol"
+ >}</a
+ ><a name="23867"
> </a
- ><a name="23871" class="Symbol"
+ ><a name="23868" class="Symbol"
>→</a
- ><a name="23872"
+ ><a name="23869"
> </a
- ><a name="23873" href="StlcProp.html#23852" class="Bound"
+ ><a name="23870" href="Maps.html#10265" class="Function"
+ >∅</a
+ ><a name="23871"
+ > </a
+ ><a name="23872" href="Stlc.html#6070" class="Datatype Operator"
+ >⊢</a
+ ><a name="23873"
+ > </a
+ ><a name="23874" href="StlcProp.html#23861" class="Bound"
>M</a
- ><a name="23874"
+ ><a name="23875"
> </a
- ><a name="23875" href="Stlc.html#2287" class="Datatype Operator"
- >⟹*</a
+ ><a name="23876" href="Stlc.html#6070" class="Datatype Operator"
+ >∶</a
><a name="23877"
> </a
- ><a name="23878" href="StlcProp.html#23854" class="Bound"
- >N</a
+ ><a name="23878" href="StlcProp.html#23865" class="Bound"
+ >A</a
><a name="23879"
> </a
><a name="23880" class="Symbol"
>→</a
><a name="23881"
> </a
- ><a name="23882" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#414" class="Function Operator"
- >¬</a
+ ><a name="23882" href="StlcProp.html#23861" class="Bound"
+ >M</a
><a name="23883"
> </a
- ><a name="23884" class="Symbol"
- >(</a
- ><a name="23885" href="StlcProp.html#23670" class="Function"
- >Stuck</a
+ ><a name="23884" href="Stlc.html#5245" class="Datatype Operator"
+ >⟹*</a
+ ><a name="23886"
+ > </a
+ ><a name="23887" href="StlcProp.html#23863" class="Bound"
+ >N</a
+ ><a name="23888"
+ > </a
+ ><a name="23889" class="Symbol"
+ >→</a
><a name="23890"
> </a
- ><a name="23891" href="StlcProp.html#23854" class="Bound"
+ ><a name="23891" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#414" class="Function Operator"
+ >¬</a
+ ><a name="23892"
+ > </a
+ ><a name="23893" class="Symbol"
+ >(</a
+ ><a name="23894" href="StlcProp.html#23679" class="Function"
+ >Stuck</a
+ ><a name="23899"
+ > </a
+ ><a name="23900" href="StlcProp.html#23863" class="Bound"
>N</a
- ><a name="23892" class="Symbol"
+ ><a name="23901" class="Symbol"
>)</a
- ><a name="23893"
+ ><a name="23902"
>
</a
- ><a name="23894" href="StlcProp.html#23836" class="Function"
+ ><a name="23903" href="StlcProp.html#23845" class="Function"
>Soundness′</a
- ><a name="23904"
- > </a
- ><a name="23905" href="StlcProp.html#23905" class="Bound"
- >⊢M</a
- ><a name="23907"
- > </a
- ><a name="23908" class="Symbol"
- >(</a
- ><a name="23909" href="StlcProp.html#23909" class="Bound"
- >M</a
- ><a name="23910"
- > </a
- ><a name="23911" href="Stlc.html#2320" class="InductiveConstructor Operator"
- >∎</a
- ><a name="23912" class="Symbol"
- >)</a
><a name="23913"
> </a
- ><a name="23914" class="Symbol"
+ ><a name="23914" href="StlcProp.html#23914" class="Bound"
+ >⊢M</a
+ ><a name="23916"
+ > </a
+ ><a name="23917" class="Symbol"
>(</a
- ><a name="23915" href="StlcProp.html#23915" class="Bound"
- >¬M⟹N</a
+ ><a name="23918" href="StlcProp.html#23918" class="Bound"
+ >M</a
><a name="23919"
> </a
- ><a name="23920" href="https://agda.github.io/agda-stdlib/Data.Product.html#509" class="InductiveConstructor Operator"
- >,</a
- ><a name="23921"
- > </a
- ><a name="23922" href="StlcProp.html#23922" class="Bound"
- >¬ValueM</a
- ><a name="23929" class="Symbol"
+ ><a name="23920" href="Stlc.html#5278" class="InductiveConstructor Operator"
+ >∎</a
+ ><a name="23921" class="Symbol"
>)</a
+ ><a name="23922"
+ > </a
+ ><a name="23923" class="Symbol"
+ >(</a
+ ><a name="23924" href="StlcProp.html#23924" class="Bound"
+ >¬M⟹N</a
+ ><a name="23928"
+ > </a
+ ><a name="23929" href="https://agda.github.io/agda-stdlib/Data.Product.html#509" class="InductiveConstructor Operator"
+ >,</a
><a name="23930"
> </a
- ><a name="23931" class="Keyword"
- >with</a
- ><a name="23935"
+ ><a name="23931" href="StlcProp.html#23931" class="Bound"
+ >¬ValueM</a
+ ><a name="23938" class="Symbol"
+ >)</a
+ ><a name="23939"
> </a
- ><a name="23936" href="StlcProp.html#2024" class="Function"
- >progress</a
+ ><a name="23940" class="Keyword"
+ >with</a
><a name="23944"
> </a
- ><a name="23945" href="StlcProp.html#23905" class="Bound"
- >⊢M</a
- ><a name="23947"
- >
-</a
- ><a name="23948" class="Symbol"
- >...</a
- ><a name="23951"
- > </a
- ><a name="23952" class="Symbol"
- >|</a
+ ><a name="23945" href="StlcProp.html#2024" class="Function"
+ >progress</a
><a name="23953"
> </a
- ><a name="23954" href="StlcProp.html#1947" class="InductiveConstructor"
- >steps</a
- ><a name="23959"
- > </a
- ><a name="23960" href="StlcProp.html#23960" class="Bound"
- >M⟹N</a
- ><a name="23963"
- > </a
- ><a name="23965" class="Symbol"
- >=</a
- ><a name="23966"
- > </a
- ><a name="23967" href="StlcProp.html#23915" class="Bound"
- >¬M⟹N</a
- ><a name="23971"
- > </a
- ><a name="23972" href="StlcProp.html#23960" class="Bound"
- >M⟹N</a
- ><a name="23975"
+ ><a name="23954" href="StlcProp.html#23914" class="Bound"
+ >⊢M</a
+ ><a name="23956"
>
</a
- ><a name="23976" class="Symbol"
+ ><a name="23957" class="Symbol"
>...</a
- ><a name="23979"
+ ><a name="23960"
> </a
- ><a name="23980" class="Symbol"
+ ><a name="23961" class="Symbol"
>|</a
- ><a name="23981"
+ ><a name="23962"
> </a
- ><a name="23982" href="StlcProp.html#1986" class="InductiveConstructor"
- >done</a
- ><a name="23986"
+ ><a name="23963" href="StlcProp.html#1947" class="InductiveConstructor"
+ >steps</a
+ ><a name="23968"
> </a
- ><a name="23987" href="StlcProp.html#23987" class="Bound"
- >ValueM</a
- ><a name="23993"
+ ><a name="23969" href="StlcProp.html#23969" class="Bound"
+ >M⟹N</a
+ ><a name="23972"
> </a
- ><a name="23995" class="Symbol"
+ ><a name="23974" class="Symbol"
>=</a
- ><a name="23996"
+ ><a name="23975"
> </a
- ><a name="23997" href="StlcProp.html#23922" class="Bound"
- >¬ValueM</a
- ><a name="24004"
+ ><a name="23976" href="StlcProp.html#23924" class="Bound"
+ >¬M⟹N</a
+ ><a name="23980"
> </a
- ><a name="24005" href="StlcProp.html#23987" class="Bound"
- >ValueM</a
- ><a name="24011"
+ ><a name="23981" href="StlcProp.html#23969" class="Bound"
+ >M⟹N</a
+ ><a name="23984"
>
</a
- ><a name="24012" href="StlcProp.html#23836" class="Function"
+ ><a name="23985" class="Symbol"
+ >...</a
+ ><a name="23988"
+ > </a
+ ><a name="23989" class="Symbol"
+ >|</a
+ ><a name="23990"
+ > </a
+ ><a name="23991" href="StlcProp.html#1986" class="InductiveConstructor"
+ >done</a
+ ><a name="23995"
+ > </a
+ ><a name="23996" href="StlcProp.html#23996" class="Bound"
+ >ValueM</a
+ ><a name="24002"
+ > </a
+ ><a name="24004" class="Symbol"
+ >=</a
+ ><a name="24005"
+ > </a
+ ><a name="24006" href="StlcProp.html#23931" class="Bound"
+ >¬ValueM</a
+ ><a name="24013"
+ > </a
+ ><a name="24014" href="StlcProp.html#23996" class="Bound"
+ >ValueM</a
+ ><a name="24020"
+ >
+</a
+ ><a name="24021" href="StlcProp.html#23845" class="Function"
>Soundness′</a
- ><a name="24022"
+ ><a name="24031"
> </a
- ><a name="24023" class="Symbol"
+ ><a name="24032" class="Symbol"
>{</a
- ><a name="24024" href="StlcProp.html#24024" class="Bound"
+ ><a name="24033" href="StlcProp.html#24033" class="Bound"
>L</a
- ><a name="24025" class="Symbol"
+ ><a name="24034" class="Symbol"
>}</a
- ><a name="24026"
+ ><a name="24035"
> </a
- ><a name="24027" class="Symbol"
+ ><a name="24036" class="Symbol"
>{</a
- ><a name="24028" href="StlcProp.html#24028" class="Bound"
+ ><a name="24037" href="StlcProp.html#24037" class="Bound"
>N</a
- ><a name="24029" class="Symbol"
- >}</a
- ><a name="24030"
- > </a
- ><a name="24031" class="Symbol"
- >{</a
- ><a name="24032" href="StlcProp.html#24032" class="Bound"
- >A</a
- ><a name="24033" class="Symbol"
- >}</a
- ><a name="24034"
- > </a
- ><a name="24035" href="StlcProp.html#24035" class="Bound"
- >⊢L</a
- ><a name="24037"
- > </a
><a name="24038" class="Symbol"
+ >}</a
+ ><a name="24039"
+ > </a
+ ><a name="24040" class="Symbol"
+ >{</a
+ ><a name="24041" href="StlcProp.html#24041" class="Bound"
+ >A</a
+ ><a name="24042" class="Symbol"
+ >}</a
+ ><a name="24043"
+ > </a
+ ><a name="24044" href="StlcProp.html#24044" class="Bound"
+ >⊢L</a
+ ><a name="24046"
+ > </a
+ ><a name="24047" class="Symbol"
>(</a
- ><a name="24039" href="Stlc.html#2340" class="InductiveConstructor Operator"
+ ><a name="24048" href="Stlc.html#5298" class="InductiveConstructor Operator"
>_⟹⟨_⟩_</a
- ><a name="24045"
+ ><a name="24054"
> </a
- ><a name="24046" class="DottedPattern Symbol"
+ ><a name="24055" class="DottedPattern Symbol"
>.</a
- ><a name="24047" href="StlcProp.html#24024" class="DottedPattern Bound"
+ ><a name="24056" href="StlcProp.html#24033" class="DottedPattern Bound"
>L</a
- ><a name="24048"
- > </a
- ><a name="24049" class="Symbol"
- >{</a
- ><a name="24050" href="StlcProp.html#24050" class="Bound"
- >M</a
- ><a name="24051" class="Symbol"
- >}</a
- ><a name="24052"
- > </a
- ><a name="24053" class="Symbol"
- >{</a
- ><a name="24054" class="DottedPattern Symbol"
- >.</a
- ><a name="24055" href="StlcProp.html#24028" class="DottedPattern Bound"
- >N</a
- ><a name="24056" class="Symbol"
- >}</a
><a name="24057"
> </a
- ><a name="24058" href="StlcProp.html#24058" class="Bound"
- >L⟹M</a
+ ><a name="24058" class="Symbol"
+ >{</a
+ ><a name="24059" href="StlcProp.html#24059" class="Bound"
+ >M</a
+ ><a name="24060" class="Symbol"
+ >}</a
><a name="24061"
> </a
- ><a name="24062" href="StlcProp.html#24062" class="Bound"
+ ><a name="24062" class="Symbol"
+ >{</a
+ ><a name="24063" class="DottedPattern Symbol"
+ >.</a
+ ><a name="24064" href="StlcProp.html#24037" class="DottedPattern Bound"
+ >N</a
+ ><a name="24065" class="Symbol"
+ >}</a
+ ><a name="24066"
+ > </a
+ ><a name="24067" href="StlcProp.html#24067" class="Bound"
+ >L⟹M</a
+ ><a name="24070"
+ > </a
+ ><a name="24071" href="StlcProp.html#24071" class="Bound"
>M⟹*N</a
- ><a name="24066" class="Symbol"
+ ><a name="24075" class="Symbol"
>)</a
- ><a name="24067"
+ ><a name="24076"
> </a
- ><a name="24068" class="Symbol"
+ ><a name="24077" class="Symbol"
>=</a
- ><a name="24069"
+ ><a name="24078"
> </a
- ><a name="24070" href="StlcProp.html#23836" class="Function"
+ ><a name="24079" href="StlcProp.html#23845" class="Function"
>Soundness′</a
- ><a name="24080"
+ ><a name="24089"
> </a
- ><a name="24081" href="StlcProp.html#24099" class="Function"
+ ><a name="24090" href="StlcProp.html#24108" class="Function"
>⊢M</a
- ><a name="24083"
+ ><a name="24092"
> </a
- ><a name="24084" href="StlcProp.html#24062" class="Bound"
+ ><a name="24093" href="StlcProp.html#24071" class="Bound"
>M⟹*N</a
- ><a name="24088"
+ ><a name="24097"
>
</a
- ><a name="24091" class="Keyword"
+ ><a name="24100" class="Keyword"
>where</a
- ><a name="24096"
- >
- </a
- ><a name="24099" href="StlcProp.html#24099" class="Function"
- >⊢M</a
- ><a name="24101"
- > </a
- ><a name="24102" class="Symbol"
- >:</a
- ><a name="24103"
- > </a
- ><a name="24104" href="Maps.html#10265" class="Function"
- >∅</a
><a name="24105"
- > </a
- ><a name="24106" href="Stlc.html#3112" class="Datatype Operator"
- >⊢</a
- ><a name="24107"
- > </a
- ><a name="24108" href="StlcProp.html#24050" class="Bound"
- >M</a
- ><a name="24109"
- > </a
- ><a name="24110" href="Stlc.html#3112" class="Datatype Operator"
- >∶</a
- ><a name="24111"
- > </a
- ><a name="24112" href="StlcProp.html#24032" class="Bound"
- >A</a
- ><a name="24113"
>
</a
- ><a name="24116" href="StlcProp.html#24099" class="Function"
+ ><a name="24108" href="StlcProp.html#24108" class="Function"
>⊢M</a
+ ><a name="24110"
+ > </a
+ ><a name="24111" class="Symbol"
+ >:</a
+ ><a name="24112"
+ > </a
+ ><a name="24113" href="Maps.html#10265" class="Function"
+ >∅</a
+ ><a name="24114"
+ > </a
+ ><a name="24115" href="Stlc.html#6070" class="Datatype Operator"
+ >⊢</a
+ ><a name="24116"
+ > </a
+ ><a name="24117" href="StlcProp.html#24059" class="Bound"
+ >M</a
><a name="24118"
> </a
- ><a name="24119" class="Symbol"
- >=</a
+ ><a name="24119" href="Stlc.html#6070" class="Datatype Operator"
+ >∶</a
><a name="24120"
> </a
- ><a name="24121" href="StlcProp.html#21140" class="Function"
+ ><a name="24121" href="StlcProp.html#24041" class="Bound"
+ >A</a
+ ><a name="24122"
+ >
+ </a
+ ><a name="24125" href="StlcProp.html#24108" class="Function"
+ >⊢M</a
+ ><a name="24127"
+ > </a
+ ><a name="24128" class="Symbol"
+ >=</a
+ ><a name="24129"
+ > </a
+ ><a name="24130" href="StlcProp.html#21149" class="Function"
>preservation</a
- ><a name="24133"
+ ><a name="24142"
> </a
- ><a name="24134" href="StlcProp.html#24035" class="Bound"
+ ><a name="24143" href="StlcProp.html#24044" class="Bound"
>⊢L</a
- ><a name="24136"
+ ><a name="24145"
> </a
- ><a name="24137" href="StlcProp.html#24058" class="Bound"
+ ><a name="24146" href="StlcProp.html#24067" class="Bound"
>L⟹M</a
>
@@ -7731,65 +7731,65 @@ booleans, for brevity).
<pre class="Agda">
-<a name="28553" class="Keyword"
+<a name="28562" class="Keyword"
>data</a
- ><a name="28557"
+ ><a name="28566"
> </a
- ><a name="28558" href="StlcProp.html#28558" class="Datatype"
+ ><a name="28567" href="StlcProp.html#28567" class="Datatype"
>Type′</a
- ><a name="28563"
+ ><a name="28572"
> </a
- ><a name="28564" class="Symbol"
+ ><a name="28573" class="Symbol"
>:</a
- ><a name="28565"
+ ><a name="28574"
> </a
- ><a name="28566" class="PrimitiveType"
+ ><a name="28575" class="PrimitiveType"
>Set</a
- ><a name="28569"
+ ><a name="28578"
> </a
- ><a name="28570" class="Keyword"
+ ><a name="28579" class="Keyword"
>where</a
- ><a name="28575"
+ ><a name="28584"
>
</a
- ><a name="28578" href="StlcProp.html#28578" class="InductiveConstructor Operator"
+ ><a name="28587" href="StlcProp.html#28587" class="InductiveConstructor Operator"
>_⇒_</a
- ><a name="28581"
+ ><a name="28590"
> </a
- ><a name="28582" class="Symbol"
+ ><a name="28591" class="Symbol"
>:</a
- ><a name="28583"
+ ><a name="28592"
> </a
- ><a name="28584" href="StlcProp.html#28558" class="Datatype"
+ ><a name="28593" href="StlcProp.html#28567" class="Datatype"
>Type′</a
- ><a name="28589"
+ ><a name="28598"
> </a
- ><a name="28590" class="Symbol"
+ ><a name="28599" class="Symbol"
>→</a
- ><a name="28591"
+ ><a name="28600"
> </a
- ><a name="28592" href="StlcProp.html#28558" class="Datatype"
+ ><a name="28601" href="StlcProp.html#28567" class="Datatype"
>Type′</a
- ><a name="28597"
+ ><a name="28606"
> </a
- ><a name="28598" class="Symbol"
+ ><a name="28607" class="Symbol"
>→</a
- ><a name="28599"
+ ><a name="28608"
> </a
- ><a name="28600" href="StlcProp.html#28558" class="Datatype"
+ ><a name="28609" href="StlcProp.html#28567" class="Datatype"
>Type′</a
- ><a name="28605"
+ ><a name="28614"
>
</a
- ><a name="28608" href="StlcProp.html#28608" class="InductiveConstructor"
+ ><a name="28617" href="StlcProp.html#28617" class="InductiveConstructor"
>ℕ</a
- ><a name="28609"
+ ><a name="28618"
> </a
- ><a name="28610" class="Symbol"
+ ><a name="28619" class="Symbol"
>:</a
- ><a name="28611"
+ ><a name="28620"
> </a
- ><a name="28612" href="StlcProp.html#28558" class="Datatype"
+ ><a name="28621" href="StlcProp.html#28567" class="Datatype"
>Type′</a
>
@@ -7800,226 +7800,226 @@ plus, minus, and testing for zero.
<pre class="Agda">
-<a name="28733" class="Keyword"
+<a name="28742" class="Keyword"
>data</a
- ><a name="28737"
+ ><a name="28746"
> </a
- ><a name="28738" href="StlcProp.html#28738" class="Datatype"
+ ><a name="28747" href="StlcProp.html#28747" class="Datatype"
>Term′</a
- ><a name="28743"
+ ><a name="28752"
> </a
- ><a name="28744" class="Symbol"
+ ><a name="28753" class="Symbol"
>:</a
- ><a name="28745"
+ ><a name="28754"
> </a
- ><a name="28746" class="PrimitiveType"
+ ><a name="28755" class="PrimitiveType"
>Set</a
- ><a name="28749"
+ ><a name="28758"
> </a
- ><a name="28750" class="Keyword"
+ ><a name="28759" class="Keyword"
>where</a
- ><a name="28755"
+ ><a name="28764"
>
</a
- ><a name="28758" href="StlcProp.html#28758" class="InductiveConstructor Operator"
+ ><a name="28767" href="StlcProp.html#28767" class="InductiveConstructor Operator"
>`_</a
- ><a name="28760"
+ ><a name="28769"
> </a
- ><a name="28761" class="Symbol"
+ ><a name="28770" class="Symbol"
>:</a
- ><a name="28762"
+ ><a name="28771"
> </a
- ><a name="28763" href="Maps.html#2171" class="Datatype"
+ ><a name="28772" href="Maps.html#2171" class="Datatype"
>Id</a
- ><a name="28765"
+ ><a name="28774"
> </a
- ><a name="28766" class="Symbol"
+ ><a name="28775" class="Symbol"
>→</a
- ><a name="28767"
+ ><a name="28776"
> </a
- ><a name="28768" href="StlcProp.html#28738" class="Datatype"
+ ><a name="28777" href="StlcProp.html#28747" class="Datatype"
>Term′</a
- ><a name="28773"
+ ><a name="28782"
>
</a
- ><a name="28776" href="StlcProp.html#28776" class="InductiveConstructor Operator"
+ ><a name="28785" href="StlcProp.html#28785" class="InductiveConstructor Operator"
>λ[_∶_]_</a
- ><a name="28783"
+ ><a name="28792"
> </a
- ><a name="28784" class="Symbol"
+ ><a name="28793" class="Symbol"
>:</a
- ><a name="28785"
+ ><a name="28794"
> </a
- ><a name="28786" href="Maps.html#2171" class="Datatype"
+ ><a name="28795" href="Maps.html#2171" class="Datatype"
>Id</a
- ><a name="28788"
+ ><a name="28797"
> </a
- ><a name="28789" class="Symbol"
+ ><a name="28798" class="Symbol"
>→</a
- ><a name="28790"
+ ><a name="28799"
> </a
- ><a name="28791" href="StlcProp.html#28558" class="Datatype"
+ ><a name="28800" href="StlcProp.html#28567" class="Datatype"
>Type′</a
- ><a name="28796"
+ ><a name="28805"
> </a
- ><a name="28797" class="Symbol"
+ ><a name="28806" class="Symbol"
>→</a
- ><a name="28798"
+ ><a name="28807"
> </a
- ><a name="28799" href="StlcProp.html#28738" class="Datatype"
+ ><a name="28808" href="StlcProp.html#28747" class="Datatype"
>Term′</a
- ><a name="28804"
+ ><a name="28813"
> </a
- ><a name="28805" class="Symbol"
+ ><a name="28814" class="Symbol"
>→</a
- ><a name="28806"
+ ><a name="28815"
> </a
- ><a name="28807" href="StlcProp.html#28738" class="Datatype"
+ ><a name="28816" href="StlcProp.html#28747" class="Datatype"
>Term′</a
- ><a name="28812"
+ ><a name="28821"
>
</a
- ><a name="28815" href="StlcProp.html#28815" class="InductiveConstructor Operator"
+ ><a name="28824" href="StlcProp.html#28824" class="InductiveConstructor Operator"
>_·_</a
- ><a name="28818"
+ ><a name="28827"
> </a
- ><a name="28819" class="Symbol"
+ ><a name="28828" class="Symbol"
>:</a
- ><a name="28820"
+ ><a name="28829"
> </a
- ><a name="28821" href="StlcProp.html#28738" class="Datatype"
+ ><a name="28830" href="StlcProp.html#28747" class="Datatype"
>Term′</a
- ><a name="28826"
+ ><a name="28835"
> </a
- ><a name="28827" class="Symbol"
+ ><a name="28836" class="Symbol"
>→</a
- ><a name="28828"
+ ><a name="28837"
> </a
- ><a name="28829" href="StlcProp.html#28738" class="Datatype"
+ ><a name="28838" href="StlcProp.html#28747" class="Datatype"
>Term′</a
- ><a name="28834"
+ ><a name="28843"
> </a
- ><a name="28835" class="Symbol"
+ ><a name="28844" class="Symbol"
>→</a
- ><a name="28836"
+ ><a name="28845"
> </a
- ><a name="28837" href="StlcProp.html#28738" class="Datatype"
+ ><a name="28846" href="StlcProp.html#28747" class="Datatype"
>Term′</a
- ><a name="28842"
+ ><a name="28851"
>
</a
- ><a name="28845" href="StlcProp.html#28845" class="InductiveConstructor Operator"
+ ><a name="28854" href="StlcProp.html#28854" class="InductiveConstructor Operator"
>‶_</a
- ><a name="28847"
+ ><a name="28856"
> </a
- ><a name="28848" class="Symbol"
+ ><a name="28857" class="Symbol"
>:</a
- ><a name="28849"
+ ><a name="28858"
> </a
- ><a name="28850" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Nat.html#97" class="Datatype"
+ ><a name="28859" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Nat.html#97" class="Datatype"
>Data.Nat.ℕ</a
- ><a name="28860"
+ ><a name="28869"
> </a
- ><a name="28861" class="Symbol"
+ ><a name="28870" class="Symbol"
>→</a
- ><a name="28862"
+ ><a name="28871"
> </a
- ><a name="28863" href="StlcProp.html#28738" class="Datatype"
+ ><a name="28872" href="StlcProp.html#28747" class="Datatype"
>Term′</a
- ><a name="28868"
+ ><a name="28877"
>
</a
- ><a name="28871" href="StlcProp.html#28871" class="InductiveConstructor Operator"
+ ><a name="28880" href="StlcProp.html#28880" class="InductiveConstructor Operator"
>_+_</a
- ><a name="28874"
+ ><a name="28883"
> </a
- ><a name="28875" class="Symbol"
+ ><a name="28884" class="Symbol"
>:</a
- ><a name="28876"
+ ><a name="28885"
> </a
- ><a name="28877" href="StlcProp.html#28738" class="Datatype"
+ ><a name="28886" href="StlcProp.html#28747" class="Datatype"
>Term′</a
- ><a name="28882"
+ ><a name="28891"
> </a
- ><a name="28883" class="Symbol"
+ ><a name="28892" class="Symbol"
>→</a
- ><a name="28884"
+ ><a name="28893"
> </a
- ><a name="28885" href="StlcProp.html#28738" class="Datatype"
+ ><a name="28894" href="StlcProp.html#28747" class="Datatype"
>Term′</a
- ><a name="28890"
+ ><a name="28899"
> </a
- ><a name="28891" class="Symbol"
+ ><a name="28900" class="Symbol"
>→</a
- ><a name="28892"
+ ><a name="28901"
> </a
- ><a name="28893" href="StlcProp.html#28738" class="Datatype"
+ ><a name="28902" href="StlcProp.html#28747" class="Datatype"
>Term′</a
- ><a name="28898"
+ ><a name="28907"
>
</a
- ><a name="28901" href="StlcProp.html#28901" class="InductiveConstructor Operator"
+ ><a name="28910" href="StlcProp.html#28910" class="InductiveConstructor Operator"
>_-_</a
- ><a name="28904"
+ ><a name="28913"
> </a
- ><a name="28905" class="Symbol"
+ ><a name="28914" class="Symbol"
>:</a
- ><a name="28906"
+ ><a name="28915"
> </a
- ><a name="28907" href="StlcProp.html#28738" class="Datatype"
+ ><a name="28916" href="StlcProp.html#28747" class="Datatype"
>Term′</a
- ><a name="28912"
+ ><a name="28921"
> </a
- ><a name="28913" class="Symbol"
+ ><a name="28922" class="Symbol"
>→</a
- ><a name="28914"
+ ><a name="28923"
> </a
- ><a name="28915" href="StlcProp.html#28738" class="Datatype"
+ ><a name="28924" href="StlcProp.html#28747" class="Datatype"
>Term′</a
- ><a name="28920"
+ ><a name="28929"
> </a
- ><a name="28921" class="Symbol"
+ ><a name="28930" class="Symbol"
>→</a
- ><a name="28922"
+ ><a name="28931"
> </a
- ><a name="28923" href="StlcProp.html#28738" class="Datatype"
+ ><a name="28932" href="StlcProp.html#28747" class="Datatype"
>Term′</a
- ><a name="28928"
+ ><a name="28937"
>
</a
- ><a name="28931" href="StlcProp.html#28931" class="InductiveConstructor Operator"
+ ><a name="28940" href="StlcProp.html#28940" class="InductiveConstructor Operator"
>if0_then_else_</a
- ><a name="28945"
+ ><a name="28954"
> </a
- ><a name="28946" class="Symbol"
+ ><a name="28955" class="Symbol"
>:</a
- ><a name="28947"
+ ><a name="28956"
> </a
- ><a name="28948" href="StlcProp.html#28738" class="Datatype"
+ ><a name="28957" href="StlcProp.html#28747" class="Datatype"
>Term′</a
- ><a name="28953"
+ ><a name="28962"
> </a
- ><a name="28954" class="Symbol"
+ ><a name="28963" class="Symbol"
>→</a
- ><a name="28955"
+ ><a name="28964"
> </a
- ><a name="28956" href="StlcProp.html#28738" class="Datatype"
+ ><a name="28965" href="StlcProp.html#28747" class="Datatype"
>Term′</a
- ><a name="28961"
+ ><a name="28970"
> </a
- ><a name="28962" class="Symbol"
+ ><a name="28971" class="Symbol"
>→</a
- ><a name="28963"
+ ><a name="28972"
> </a
- ><a name="28964" href="StlcProp.html#28738" class="Datatype"
+ ><a name="28973" href="StlcProp.html#28747" class="Datatype"
>Term′</a
- ><a name="28969"
+ ><a name="28978"
> </a
- ><a name="28970" class="Symbol"
+ ><a name="28979" class="Symbol"
>→</a
- ><a name="28971"
+ ><a name="28980"
> </a
- ><a name="28972" href="StlcProp.html#28738" class="Datatype"
+ ><a name="28981" href="StlcProp.html#28747" class="Datatype"
>Term′</a
>
diff --git a/src/Stlc.lagda b/src/Stlc.lagda
index 9abc392d..6cfc0fa1 100644
--- a/src/Stlc.lagda
+++ b/src/Stlc.lagda
@@ -70,7 +70,7 @@ data Type : Set where
\end{code}
Terms have six constructs. Three are for the core lambda calculus:
- * Variables, `\` x`
+ * Variables, `` ` x ``
* Abstractions, `λ[ x ∶ A ] N`
* Applications, `L · M`
and three are for the base type, booleans:
@@ -285,7 +285,7 @@ outermost term is now `if_then_else_`, which is typed using `𝔹-E`. The
?2 : ∅ , x ∶ 𝔹 ⊢ true ∶ 𝔹
Again we fill in the three holes by typing C-c C-r in each. Agda observes
-that `\` x`, `false`, and `true` are typed using `Ax`, `𝔹-I₂`, and
+that `` ` x ``, `false`, and `true` are typed using `Ax`, `𝔹-I₂`, and
`𝔹-I₁` respectively. The `Ax` rule in turn takes an argument, to show
that `(∅ , x ∶ 𝔹) x = just 𝔹`, which can in turn be specified with a
hole. After filling in all holes, the term is as above.
diff --git a/src/StlcProp.lagda b/src/StlcProp.lagda
index 6b9fbddb..d717c5ab 100644
--- a/src/StlcProp.lagda
+++ b/src/StlcProp.lagda
@@ -266,7 +266,7 @@ _Proof_: We show, by induction on the proof that `x` appears
free in `M`, that, for all contexts `Γ`, if `M` is well
typed under `Γ`, then `Γ` assigns some type to `x`.
- - If the last rule used was `free-\``, then `M = \` x`, and from
+ - If the last rule used was `` free-` ``, then `M = `` `x ``, and from
the assumption that `M` is well typed under `Γ` we have
immediately that `Γ` assigns a type to `x`.
@@ -452,7 +452,7 @@ we show that if `∅ ⊢ V ∶ A` then `Γ ⊢ N [ x := V ] ∶ B`.
- If `N` is a variable there are two cases to consider,
depending on whether `N` is `x` or some other variable.
- - If `N = \` x`, then from `Γ , x ∶ A ⊢ x ∶ B`
+ - If `N = `` `x ``, then from `Γ , x ∶ A ⊢ x ∶ B`
we know that looking up `x` in `Γ , x : A` gives
`just B`, but we already know it gives `just A`;
applying injectivity for `just` we conclude that `A ≡ B`.