fix two errors in the hott library

This commit is contained in:
Floris van Doorn 2018-09-20 01:48:55 +02:00
parent 183ca62cc1
commit 98fb55e428
2 changed files with 3 additions and 3 deletions

View file

@ -12,7 +12,7 @@ a^n is used for the first, but users can locally redefine it to gpow when needed
Note: power adopts the convention that 0^0=1.
-/
import types.nat.basic types.int.basic .homomorphism .group_theory
open algebra
open algebra eq
namespace algebra
variables {A B : Type}
@ -172,7 +172,7 @@ theorem gpow_comm (a : A) (i j : ) : gpow a i * gpow a j = gpow a j * gpow a
by rewrite [-*gpow_add, add.comm]
lemma gpow_neg (a : A) : Π(n : ), gpow a (-n) = (gpow a n)⁻¹
| (of_nat n) := by cases n with n; rewrite [gpow_zero,one_inv]; reflexivity
| (of_nat n) := begin cases n with n, exact !one_inv⁻¹, reflexivity end
| -[1+n] := by rewrite [↑gpow at {2}, inv_inv]
lemma inv_gpow (a : A) : Π(n : ), gpow a⁻¹ n = (gpow a n)⁻¹

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@ -192,7 +192,7 @@ begin
{ exact equiv_of_pequiv (freudenthal_homotopy_group_pequiv H A)},
{ intro g h,
refine _ ⬝ !homotopy_group_pequiv_loop_ptrunc_inv_con,
apply ap !homotopy_group_pequiv_loop_ptrunc⁻¹ᵉ*,
refine ap !homotopy_group_pequiv_loop_ptrunc⁻¹ᵉ* _,
refine ap (loopn_pequiv_loopn _ _) _ ⬝ !loopn_pequiv_loopn_con,
refine ap !homotopy_group_pequiv_loop_ptrunc _ ⬝ !homotopy_group_pequiv_loop_ptrunc_con,
apply homotopy_group_succ_in_con}