feat(hott): minor changes

hott/algebra/homotopy_group.hlean

@@ -19,8 +19,8 @@ namespace eq
   definition homotopy_group [reducible] (n : ℕ) (A : Type*) : Type :=
   phomotopy_group n A
 
-  notation `π*[`:95 n:0 `] `:0 := phomotopy_group n
-  notation `π[`:95  n:0 `] `:0 :=  homotopy_group n
+  notation `π*[`:95 n:0 `]`:0 := phomotopy_group n
+  notation `π[`:95  n:0 `]`:0 :=  homotopy_group n
 
   definition group_homotopy_group [instance] [constructor] [reducible] (n : ℕ) (A : Type*)
     : group (π[succ n] A) :=
@@ -126,8 +126,8 @@ namespace eq
   definition homotopy_group_functor (n : ℕ) {A B : Type*} (f : A →* B) : π[n] A → π[n] B :=
   phomotopy_group_functor n f
 
-  notation `π→*[`:95 n:0 `] `:0 := phomotopy_group_functor n
-  notation `π→[`:95  n:0 `] `:0 :=  homotopy_group_functor n
+  notation `π→*[`:95 n:0 `]`:0 := phomotopy_group_functor n
+  notation `π→[`:95  n:0 `]`:0 :=  homotopy_group_functor n
 
   definition phomotopy_group_functor_phomotopy [constructor] (n : ℕ) {A B : Type*} {f g : A →* B}
     (p : f ~* g) : π→*[n] f ~* π→*[n] g :=
@@ -267,6 +267,6 @@ namespace eq
     exact ap tr !con_inv
   end
 
-  notation `π→g[`:95  n:0 ` +1] `:0 f:95 := homotopy_group_homomorphism n f
+  notation `π→g[`:95 n:0 ` +1]`:0 := homotopy_group_homomorphism n
 
 end eq

hott/hit/two_quotient.hlean

@@ -1,4 +1,4 @@
-/-
+ /-
 Copyright (c) 2015 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 

hott/homotopy/LES_of_homotopy_groups.hlean

@@ -76,7 +76,6 @@ We get the long exact sequence of homotopy groups by taking the set-truncation o
 import .chain_complex algebra.homotopy_group eq2
 
 open eq pointed sigma fiber equiv is_equiv sigma.ops is_trunc nat trunc algebra function sum
-
 /--------------
     PART 1
  --------------/

hott/homotopy/homotopy_group.hlean

@@ -53,6 +53,15 @@ namespace is_trunc
     [H : is_conn_fun n f] (H2 : k ≤ n) : is_contr (π[k] (pfiber f)) :=
   @(trivial_homotopy_group_of_is_conn (pfiber f) H2) (H pt)
 
+  theorem homotopy_group_trunc_of_le (A : Type*) (n k : ℕ) (H : k ≤ n)
+    : π*[k] (ptrunc n A) ≃* π*[k] A :=
+  begin
+    refine !phomotopy_group_pequiv_loop_ptrunc ⬝e* _,
+    refine loopn_pequiv_loopn _ (ptrunc_ptrunc_pequiv_left _ _) ⬝e* _,
+    exact of_nat_le_of_nat H,
+    exact !phomotopy_group_pequiv_loop_ptrunc⁻¹ᵉ*,
+  end
+
   /- Corollaries of the LES of homotopy groups -/
   local attribute comm_group.to_group [coercion]
   local attribute is_equiv_tinverse [instance]

hott/homotopy/wedge.hlean

@@ -3,7 +3,7 @@ Copyright (c) 2016 Jakob von Raumer. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jakob von Raumer, Ulrik Buchholtz
 
-The Wedge Sum of Two pType Types
+The Wedge Sum of Two Pointed Types
 -/
 import hit.pointed_pushout .connectedness types.unit
 

hott/init/path.hlean

@@ -49,7 +49,7 @@ namespace eq
   definition con_idp [unfold_full] (p : x = y) : p ⬝ idp = p :=
   idp
 
-  -- The identity path is a right unit.
+  -- The identity path is a left unit.
   definition idp_con [unfold 4] (p : x = y) : idp ⬝ p = p :=
   by induction p; reflexivity
 

hott/types/fin.hlean

@@ -39,6 +39,8 @@ begin
   intro p, induction p, apply ap (mk i), apply !is_prop.elim
 end
 
+definition fin_eq := @eq_of_veq
+
 definition eq_of_veq_refl (i : fin n) : eq_of_veq (refl (val i)) = idp :=
 !is_prop.elim
 

library/data/set/basic.lean

@@ -496,7 +496,7 @@ end
 /- set difference -/
 
 definition diff (s t : set X) : set X := {x ∈ s | x ∉ t}
-infix `\`:70 := diff
+infix ` \ `:70 := diff
 
 theorem mem_diff {s t : set X} {x : X} (H1 : x ∈ s) (H2 : x ∉ t) : x ∈ s \ t :=
 and.intro H1 H2