small fix to Stlc
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2 changed files with 129 additions and 129 deletions
256
out/Stlc.md
256
out/Stlc.md
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@ -5313,7 +5313,7 @@ Here are the above derivations formalised in Agda.
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</pre>
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## Interaction with Agda
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#### Interaction with Agda
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Construction of a type derivation is best done interactively.
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Start with the declaration:
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@ -5359,245 +5359,245 @@ In other words, no type `A` is the type of this term.
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<pre class="Agda">
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<a name="25000" href="Stlc.html#25000" class="Function"
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<a name="25002" href="Stlc.html#25002" class="Function"
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>contradiction</a
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><a name="25013"
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> </a
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><a name="25014" class="Symbol"
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>:</a
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><a name="25015"
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> </a
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><a name="25016" class="Symbol"
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>∀</a
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>:</a
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><a name="25017"
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> </a
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><a name="25018" class="Symbol"
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>∀</a
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><a name="25019"
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> </a
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><a name="25020" class="Symbol"
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>{</a
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><a name="25019" href="Stlc.html#25019" class="Bound"
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>A</a
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><a name="25020"
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> </a
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><a name="25021" href="Stlc.html#25021" class="Bound"
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>B</a
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><a name="25022" class="Symbol"
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>}</a
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><a name="25023"
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>A</a
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><a name="25022"
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> </a
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><a name="25023" href="Stlc.html#25023" class="Bound"
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>B</a
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><a name="25024" class="Symbol"
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>→</a
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>}</a
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><a name="25025"
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> </a
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><a name="25026" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#414" class="Function Operator"
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>¬</a
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><a name="25026" class="Symbol"
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>→</a
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><a name="25027"
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> </a
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><a name="25028" class="Symbol"
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>(</a
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><a name="25029" href="Stlc.html#2601" class="InductiveConstructor"
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>𝔹</a
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><a name="25030"
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><a name="25028" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#414" class="Function Operator"
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>¬</a
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><a name="25029"
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> </a
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><a name="25031" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#83" class="Datatype Operator"
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>≡</a
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><a name="25030" class="Symbol"
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>(</a
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><a name="25031" href="Stlc.html#2601" class="InductiveConstructor"
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>𝔹</a
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><a name="25032"
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> </a
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><a name="25033" href="Stlc.html#25019" class="Bound"
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>A</a
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><a name="25033" href="https://agda.github.io/agda-stdlib/Agda.Builtin.Equality.html#83" class="Datatype Operator"
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>≡</a
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><a name="25034"
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> </a
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><a name="25035" href="Stlc.html#2574" class="InductiveConstructor Operator"
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>⇒</a
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><a name="25035" href="Stlc.html#25021" class="Bound"
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>A</a
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><a name="25036"
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> </a
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><a name="25037" href="Stlc.html#25021" class="Bound"
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><a name="25037" href="Stlc.html#2574" class="InductiveConstructor Operator"
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>⇒</a
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><a name="25038"
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> </a
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><a name="25039" href="Stlc.html#25023" class="Bound"
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>B</a
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><a name="25038" class="Symbol"
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><a name="25040" class="Symbol"
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>)</a
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><a name="25039"
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><a name="25041"
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>
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</a
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><a name="25040" href="Stlc.html#25000" class="Function"
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><a name="25042" href="Stlc.html#25002" class="Function"
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>contradiction</a
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><a name="25053"
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><a name="25055"
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> </a
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><a name="25054" class="Symbol"
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><a name="25056" class="Symbol"
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>()</a
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><a name="25056"
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><a name="25058"
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>
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</a
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><a name="25058" href="Stlc.html#25058" class="Function"
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><a name="25060" href="Stlc.html#25060" class="Function"
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>notyping</a
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><a name="25066"
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> </a
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><a name="25067" class="Symbol"
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>:</a
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><a name="25068"
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> </a
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><a name="25069" class="Symbol"
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>∀</a
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>:</a
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><a name="25070"
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> </a
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><a name="25071" class="Symbol"
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>{</a
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><a name="25072" href="Stlc.html#25072" class="Bound"
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>A</a
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><a name="25073" class="Symbol"
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>}</a
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><a name="25074"
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>∀</a
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><a name="25072"
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> </a
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><a name="25073" class="Symbol"
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>{</a
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><a name="25074" href="Stlc.html#25074" class="Bound"
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>A</a
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><a name="25075" class="Symbol"
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>→</a
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>}</a
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><a name="25076"
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> </a
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><a name="25077" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#414" class="Function Operator"
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>¬</a
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><a name="25077" class="Symbol"
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>→</a
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><a name="25078"
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> </a
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><a name="25079" class="Symbol"
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>(</a
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><a name="25080" href="Maps.html#10265" class="Function"
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>∅</a
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><a name="25081"
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><a name="25079" href="https://agda.github.io/agda-stdlib/Relation.Nullary.html#414" class="Function Operator"
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>¬</a
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><a name="25080"
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> </a
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><a name="25082" href="Stlc.html#21560" class="Datatype Operator"
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>⊢</a
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><a name="25081" class="Symbol"
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>(</a
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><a name="25082" href="Maps.html#10265" class="Function"
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>∅</a
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><a name="25083"
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> </a
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><a name="25084" href="Stlc.html#3663" class="InductiveConstructor Operator"
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>λ[</a
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><a name="25086"
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><a name="25084" href="Stlc.html#21560" class="Datatype Operator"
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>⊢</a
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><a name="25085"
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> </a
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><a name="25087" href="Stlc.html#5671" class="Function"
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>x</a
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><a name="25086" href="Stlc.html#3663" class="InductiveConstructor Operator"
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>λ[</a
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><a name="25088"
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> </a
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><a name="25089" href="Stlc.html#3663" class="InductiveConstructor Operator"
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>∶</a
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><a name="25089" href="Stlc.html#5671" class="Function"
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>x</a
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><a name="25090"
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> </a
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><a name="25091" href="Stlc.html#2601" class="InductiveConstructor"
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>𝔹</a
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><a name="25091" href="Stlc.html#3663" class="InductiveConstructor Operator"
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>∶</a
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><a name="25092"
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> </a
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><a name="25093" href="Stlc.html#3663" class="InductiveConstructor Operator"
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>]</a
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><a name="25093" href="Stlc.html#2601" class="InductiveConstructor"
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>𝔹</a
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><a name="25094"
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> </a
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><a name="25095" href="Stlc.html#3663" class="InductiveConstructor Operator"
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>λ[</a
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><a name="25097"
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>]</a
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><a name="25096"
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> </a
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><a name="25098" href="Stlc.html#5673" class="Function"
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>y</a
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><a name="25097" href="Stlc.html#3663" class="InductiveConstructor Operator"
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>λ[</a
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><a name="25099"
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> </a
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><a name="25100" href="Stlc.html#3663" class="InductiveConstructor Operator"
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>∶</a
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><a name="25100" href="Stlc.html#5673" class="Function"
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>y</a
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><a name="25101"
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> </a
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><a name="25102" href="Stlc.html#2601" class="InductiveConstructor"
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>𝔹</a
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><a name="25102" href="Stlc.html#3663" class="InductiveConstructor Operator"
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>∶</a
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><a name="25103"
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> </a
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><a name="25104" href="Stlc.html#3663" class="InductiveConstructor Operator"
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>]</a
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><a name="25104" href="Stlc.html#2601" class="InductiveConstructor"
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>𝔹</a
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><a name="25105"
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> </a
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><a name="25106" href="Stlc.html#3647" class="InductiveConstructor"
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>`</a
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><a name="25106" href="Stlc.html#3663" class="InductiveConstructor Operator"
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>]</a
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><a name="25107"
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> </a
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><a name="25108" href="Stlc.html#5671" class="Function"
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>x</a
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><a name="25108" href="Stlc.html#3647" class="InductiveConstructor"
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>`</a
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><a name="25109"
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> </a
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><a name="25110" href="Stlc.html#3699" class="InductiveConstructor Operator"
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>·</a
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><a name="25110" href="Stlc.html#5671" class="Function"
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>x</a
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><a name="25111"
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> </a
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><a name="25112" href="Stlc.html#3647" class="InductiveConstructor"
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>`</a
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><a name="25112" href="Stlc.html#3699" class="InductiveConstructor Operator"
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>·</a
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><a name="25113"
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> </a
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><a name="25114" href="Stlc.html#5673" class="Function"
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>y</a
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><a name="25114" href="Stlc.html#3647" class="InductiveConstructor"
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>`</a
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><a name="25115"
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> </a
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><a name="25116" href="Stlc.html#21560" class="Datatype Operator"
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>∶</a
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><a name="25116" href="Stlc.html#5673" class="Function"
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>y</a
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><a name="25117"
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> </a
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><a name="25118" href="Stlc.html#25072" class="Bound"
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><a name="25118" href="Stlc.html#21560" class="Datatype Operator"
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>∶</a
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><a name="25119"
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> </a
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><a name="25120" href="Stlc.html#25074" class="Bound"
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>A</a
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><a name="25119" class="Symbol"
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><a name="25121" class="Symbol"
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>)</a
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><a name="25120"
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><a name="25122"
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>
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</a
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><a name="25121" href="Stlc.html#25058" class="Function"
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><a name="25123" href="Stlc.html#25060" class="Function"
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>notyping</a
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><a name="25129"
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><a name="25131"
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> </a
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><a name="25130" class="Symbol"
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><a name="25132" class="Symbol"
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>(</a
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><a name="25131" href="Stlc.html#21658" class="InductiveConstructor"
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><a name="25133" href="Stlc.html#21658" class="InductiveConstructor"
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>⇒-I</a
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><a name="25134"
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><a name="25136"
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> </a
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><a name="25135" class="Symbol"
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><a name="25137" class="Symbol"
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>(</a
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><a name="25136" href="Stlc.html#21658" class="InductiveConstructor"
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><a name="25138" href="Stlc.html#21658" class="InductiveConstructor"
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>⇒-I</a
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><a name="25139"
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><a name="25141"
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> </a
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><a name="25140" class="Symbol"
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><a name="25142" class="Symbol"
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>(</a
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><a name="25141" href="Stlc.html#21735" class="InductiveConstructor"
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><a name="25143" href="Stlc.html#21735" class="InductiveConstructor"
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>⇒-E</a
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><a name="25144"
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><a name="25146"
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> </a
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><a name="25145" class="Symbol"
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><a name="25147" class="Symbol"
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>(</a
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><a name="25146" href="Stlc.html#21604" class="InductiveConstructor"
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><a name="25148" href="Stlc.html#21604" class="InductiveConstructor"
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>Ax</a
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><a name="25148"
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><a name="25150"
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> </a
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><a name="25149" href="Stlc.html#25149" class="Bound"
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><a name="25151" href="Stlc.html#25151" class="Bound"
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>Γx</a
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><a name="25151" class="Symbol"
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>)</a
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><a name="25152"
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> </a
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><a name="25153" class="Symbol"
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>)</a
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><a name="25154"
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> </a
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><a name="25155" class="Symbol"
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>(</a
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><a name="25154" href="Stlc.html#21604" class="InductiveConstructor"
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><a name="25156" href="Stlc.html#21604" class="InductiveConstructor"
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>Ax</a
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><a name="25156"
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><a name="25158"
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> </a
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><a name="25157" href="Stlc.html#25157" class="Bound"
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><a name="25159" href="Stlc.html#25159" class="Bound"
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>Γy</a
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><a name="25159" class="Symbol"
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><a name="25161" class="Symbol"
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>))))</a
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><a name="25163"
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> </a
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><a name="25164" class="Symbol"
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>=</a
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><a name="25165"
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> </a
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><a name="25166" class="Symbol"
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>=</a
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><a name="25167"
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> </a
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><a name="25167" href="Stlc.html#25000" class="Function"
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><a name="25169" href="Stlc.html#25002" class="Function"
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>contradiction</a
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><a name="25180"
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><a name="25182"
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> </a
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><a name="25181" class="Symbol"
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><a name="25183" class="Symbol"
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>(</a
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><a name="25182" href="Maps.html#11919" class="Function"
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><a name="25184" href="Maps.html#11919" class="Function"
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>just-injective</a
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><a name="25196"
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><a name="25198"
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> </a
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><a name="25197" href="Stlc.html#25149" class="Bound"
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><a name="25199" href="Stlc.html#25151" class="Bound"
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>Γx</a
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><a name="25199" class="Symbol"
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><a name="25201" class="Symbol"
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>)</a
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>
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@ -779,7 +779,7 @@ typing₂ : ∅ ⊢ two ∶ (𝔹 ⇒ 𝔹) ⇒ 𝔹 ⇒ 𝔹
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typing₂ = ⇒-I (⇒-I (⇒-E (Ax refl) (⇒-E (Ax refl) (Ax refl))))
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\end{code}
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|
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## Interaction with Agda
|
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#### Interaction with Agda
|
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|
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Construction of a type derivation is best done interactively.
|
||||
Start with the declaration:
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