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fix two errors in the hott library

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Floris van Doorn 2018-09-20 01:48:55 +02:00
parent 183ca62cc1
commit 98fb55e428
2 changed files with 3 additions and 3 deletions
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4
hott/algebra/group_power.hlean
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@ -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. Note: power adopts the convention that 0^0=1.
-/ -/
import types.nat.basic types.int.basic .homomorphism .group_theory import types.nat.basic types.int.basic .homomorphism .group_theory
open algebra open algebra eq
namespace algebra namespace algebra
variables {A B : Type} variables {A B : Type}
@ -172,7 +172,7 @@ theorem gpow_comm (a : A) (i j : ℤ) : gpow a i * gpow a j = gpow a j * gpow a
by rewrite [-*gpow_add, add.comm] by rewrite [-*gpow_add, add.comm]
lemma gpow_neg (a : A) : Π(n : ℤ), gpow a (-n) = (gpow a n)⁻¹ lemma gpow_neg (a : A) : Π(n : ℤ), 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] | -[1+n] := by rewrite [↑gpow at {2}, inv_inv]
lemma inv_gpow (a : A) : Π(n : ℤ), gpow a⁻¹ n = (gpow a n)⁻¹ lemma inv_gpow (a : A) : Π(n : ℤ), gpow a⁻¹ n = (gpow a n)⁻¹

2
hott/homotopy/freudenthal.hlean
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@ -192,7 +192,7 @@ begin
{ exact equiv_of_pequiv (freudenthal_homotopy_group_pequiv H A)}, { exact equiv_of_pequiv (freudenthal_homotopy_group_pequiv H A)},
{ intro g h, { intro g h,
refine _ ⬝ !homotopy_group_pequiv_loop_ptrunc_inv_con, 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 (loopn_pequiv_loopn _ _) _ ⬝ !loopn_pequiv_loopn_con,
refine ap !homotopy_group_pequiv_loop_ptrunc _ ⬝ !homotopy_group_pequiv_loop_ptrunc_con, refine ap !homotopy_group_pequiv_loop_ptrunc _ ⬝ !homotopy_group_pequiv_loop_ptrunc_con,
apply homotopy_group_succ_in_con} apply homotopy_group_succ_in_con}