refactor(trunc): rename namespace is_trunc.trunc_index to trunc_index

hott/book.md

@@ -22,7 +22,7 @@ The rows indicate the chapters, the columns the sections.
 | Ch 5  | - | . | ½ | - | - | . | . | ½ |   |    |    |    |    |    |    |
 | Ch 6  | . | + | + | + | + | ½ | ½ | + | ¾ | ¼  | ¾  | +  | .  |    |    |
 | Ch 7  | + | + | + | - | ¾ | - | - |   |   |    |    |    |    |    |    |
-| Ch 8  | ¾ | ¾ | - | - | ¼ | ¼ | - | - | - | -  |    |    |    |    |    |
+| Ch 8  | + | + | - | - | ¼ | ¼ | - | - | - | -  |    |    |    |    |    |
 | Ch 9  | ¾ | + | + | ½ | ¾ | ½ | - | - | - |    |    |    |    |    |    |
 | Ch 10 | - | - | - | - | - |   |   |   |   |    |    |    |    |    |    |
 | Ch 11 | - | - | - | - | - | - |   |   |   |    |    |    |    |    |    |
@@ -141,7 +141,7 @@ Chapter 8: Homotopy theory
 
 Unless otherwise noted, the files are in the folder [homotopy](homotopy/homotopy.md)
 
-- 8.1 (π_1(S^1)): [homotopy.circle](homotopy/circle.hlean) (only one of the proofs)
+- 8.1 (π_1(S^1)): [homotopy.circle](homotopy/circle.hlean) (only the encode-decode proof)
 - 8.2 (Connectedness of suspensions): [homotopy.connectedness](homotopy/connectedness.hlean) (different proof)
 - 8.3 (πk≤n of an n-connected space and π_{k<n}(S^n)): not formalized
 - 8.4 (Fiber sequences and the long exact sequence): not formalized

hott/homotopy/connectedness.hlean

@@ -275,7 +275,7 @@ namespace homotopy
   end
 
   open trunc_index
-  theorem is_conn_sphere [instance] (n : ℕ₋₁) : is_conn (n.-1) (sphere n) :=
+  theorem is_conn_sphere [instance] (n : ℕ₋₁) : is_conn (n..-1) (sphere n) :=
   begin
     induction n with n IH,
     { apply is_trunc_trunc},

hott/homotopy/smash.hlean

@@ -8,7 +8,7 @@ The Smash Product of Types
 
 import hit.pushout .wedge .cofiber .susp .sphere
 
-open eq pushout prod pointed pType is_trunc
+open eq pushout prod pointed is_trunc
 
 definition product_of_wedge [constructor] (A B : Type*) : pwedge A B →* A ×* B :=
 begin

hott/homotopy/sphere.hlean

@@ -74,9 +74,10 @@ namespace sphere_index
   definition sub_one [reducible] (n : ℕ) : ℕ₋₁ :=
   nat.rec_on n -1 (λ n k, k.+1)
 
-  postfix `.-1`:(max+1) := sub_one
+  postfix `..-1`:(max+1) := sub_one
+  -- we use a double dot to distinguish with the notation .-1 in trunc_index (of type ℕ → ℕ₋₂)
 
-  definition succ_sub_one (n : ℕ) : (nat.succ n).-1 = n :> ℕ₋₁ :=
+  definition succ_sub_one (n : ℕ) : (nat.succ n)..-1 = n :> ℕ₋₁ :=
   idp
 
 end sphere_index
@@ -85,15 +86,15 @@ open sphere_index
 namespace trunc_index
   definition sub_one [reducible] (n : ℕ₋₁) : ℕ₋₂ :=
   sphere_index.rec_on n -2 (λ n k, k.+1)
-  postfix `.-1`:(max+1) := sub_one
+  postfix `..-1`:(max+1) := sub_one
 
   definition of_sphere_index [coercion] [reducible] (n : ℕ₋₁) : ℕ₋₂ :=
-  n.-1.+1
+  n..-1.+1
 
-  definition sub_two_eq_sub_one_sub_one (n : ℕ) : n.-2 = n.-1.-1 :=
+  definition sub_two_eq_sub_one_sub_one (n : ℕ) : n.-2 = n..-1..-1 :=
   nat.rec_on n idp (λn p, ap trunc_index.succ p)
 
-  definition succ_sub_one (n : ℕ₋₁) : n.+1.-1 = n :> ℕ₋₂ :=
+  definition succ_sub_one (n : ℕ₋₁) : n.+1..-1 = n :> ℕ₋₂ :=
   idp
 
   definition of_sphere_index_of_nat (n : ℕ)
@@ -114,6 +115,8 @@ definition sphere : ℕ₋₁ → Type₀
 
 namespace sphere
 
+  export [notation] [coercion] sphere_index
+
   definition base {n : ℕ} : sphere n := north
   definition pointed_sphere [instance] [constructor] (n : ℕ) : pointed (sphere n) :=
   pointed.mk base

hott/homotopy/wedge.hlean

@@ -7,7 +7,7 @@ The Wedge Sum of Two pType Types
 -/
 import hit.pointed_pushout .connectedness
 
-open eq pushout pointed unit is_trunc.trunc_index pType
+open eq pushout pointed unit trunc_index
 
 definition pwedge (A B : Type*) : Type* := ppushout (pconst punit A) (pconst punit B)
 

hott/init/trunc.hlean

@@ -13,8 +13,6 @@ import .nat .logic .equiv .pathover
 open eq nat sigma unit sigma.ops
 --set_option class.force_new true
 
-namespace is_trunc
-
 /- Truncation levels -/
 
 inductive trunc_index : Type₀ :=
@@ -27,10 +25,7 @@ namespace is_trunc
    notation for trunc_index is -2, -1, 0, 1, ...
    from 0 and up this comes from a coercion from num to trunc_index (via ℕ)
 -/
-  notation `-1` := trunc_index.succ trunc_index.minus_two -- ISSUE: -1 gets printed as -2.+1?
+
-  notation `-2` := trunc_index.minus_two
-  postfix `.+1`:(max+1) := trunc_index.succ
-  postfix `.+2`:(max+1) := λn, (n .+1 .+1)
 notation `ℕ₋₂` := trunc_index -- input using \N-2
 
 definition has_zero_trunc_index [instance] [priority 2000] : has_zero ℕ₋₂ :=
@@ -40,10 +35,18 @@ namespace is_trunc
 has_one.mk (succ (succ (succ minus_two)))
 
 namespace trunc_index
+
+  notation `-1` := trunc_index.succ trunc_index.minus_two -- ISSUE: -1 gets printed as -2.+1?
+  notation `-2` := trunc_index.minus_two
+  postfix `.+1`:(max+1) := trunc_index.succ
+  postfix `.+2`:(max+1) := λn, (n .+1 .+1)
+
   --addition, where we add two to the result
   definition add_plus_two [reducible] (n m : ℕ₋₂) : ℕ₋₂ :=
   trunc_index.rec_on m n (λ k l, l .+1)
 
+  infix ` +2+ `:65 := trunc_index.add_plus_two
+
   -- addition of trunc_indices, where results smaller than -2 are changed to -2
   protected definition add (n m : ℕ₋₂) : ℕ₋₂ :=
   trunc_index.cases_on m
@@ -64,10 +67,12 @@ namespace is_trunc
 has_le.mk trunc_index.le
 
 attribute trunc_index.add [reducible]
-  infix ` +2+ `:65 := trunc_index.add_plus_two
+
 definition has_add_trunc_index [instance] [priority 2000] : has_add ℕ₋₂ :=
 has_add.mk trunc_index.add
 
+namespace trunc_index
+
   definition sub_two [reducible] (n : ℕ) : ℕ₋₂ :=
   nat.rec_on n -2 (λ n k, k.+1)
 
@@ -77,10 +82,9 @@ namespace is_trunc
   postfix `.-2`:(max+1) := sub_two
   postfix `.-1`:(max+1) := λn, (n .-2 .+1)
 
-  definition trunc_index.of_nat [coercion] [reducible] (n : ℕ) : ℕ₋₂ :=
+  definition of_nat [coercion] [reducible] (n : ℕ) : ℕ₋₂ :=
   n.-2.+2
 
-  namespace trunc_index
   definition succ_le_succ {n m : ℕ₋₂} (H : n ≤ m) : n.+1 ≤ m.+1 :=
   by induction H with m H IH; apply le.tr_refl; exact le.step IH
 
@@ -89,7 +93,11 @@ namespace is_trunc
   protected definition le_refl (n : ℕ₋₂) : n ≤ n :=
   le.tr_refl n
 
-  end trunc_index
+end trunc_index open trunc_index
+
+namespace is_trunc
+
+  export [notation] [coercion] trunc_index
 
   /- truncated types -/
 
@@ -112,7 +120,7 @@ end is_trunc open is_trunc
 structure is_trunc [class] (n : ℕ₋₂) (A : Type) :=
   (to_internal : is_trunc_internal n A)
 
-open nat num is_trunc.trunc_index
+open nat num trunc_index
 
 namespace is_trunc
 

hott/types/trunc.hlean

@@ -11,9 +11,7 @@ Properties of is_trunc and trunctype
 import .pointed2 ..function algebra.order types.nat.order
 
 open eq sigma sigma.ops pi function equiv trunctype
-     is_equiv prod is_trunc.trunc_index pointed nat is_trunc algebra
+     is_equiv prod pointed nat is_trunc algebra
-
-namespace is_trunc
 
 namespace trunc_index
 
@@ -201,6 +199,8 @@ namespace is_trunc
 
 end trunc_index open trunc_index
 
+namespace is_trunc
+
   variables {A B : Type} {n : ℕ₋₂}
 
   /- theorems about trunctype -/
@@ -374,7 +374,7 @@ namespace is_trunc
     { apply is_trunc_eq}
   end
 
-end is_trunc open is_trunc is_trunc.trunc_index
+end is_trunc open is_trunc
 
 namespace trunc
   variable {A : Type}