fix two errors in the hott library
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2 changed files with 3 additions and 3 deletions
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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
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Note: power adopts the convention that 0^0=1.
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-/
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import types.nat.basic types.int.basic .homomorphism .group_theory
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open algebra
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open algebra eq
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namespace algebra
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variables {A B : Type}
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@ -172,7 +172,7 @@ theorem gpow_comm (a : A) (i j : ℤ) : gpow a i * gpow a j = gpow a j * gpow a
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by rewrite [-*gpow_add, add.comm]
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lemma gpow_neg (a : A) : Π(n : ℤ), gpow a (-n) = (gpow a n)⁻¹
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| (of_nat n) := by cases n with n; rewrite [gpow_zero,one_inv]; reflexivity
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| (of_nat n) := begin cases n with n, exact !one_inv⁻¹, reflexivity end
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| -[1+n] := by rewrite [↑gpow at {2}, inv_inv]
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lemma inv_gpow (a : A) : Π(n : ℤ), gpow a⁻¹ n = (gpow a n)⁻¹
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@ -192,7 +192,7 @@ begin
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{ exact equiv_of_pequiv (freudenthal_homotopy_group_pequiv H A)},
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{ intro g h,
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refine _ ⬝ !homotopy_group_pequiv_loop_ptrunc_inv_con,
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apply ap !homotopy_group_pequiv_loop_ptrunc⁻¹ᵉ*,
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refine ap !homotopy_group_pequiv_loop_ptrunc⁻¹ᵉ* _,
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refine ap (loopn_pequiv_loopn _ _) _ ⬝ !loopn_pequiv_loopn_con,
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refine ap !homotopy_group_pequiv_loop_ptrunc _ ⬝ !homotopy_group_pequiv_loop_ptrunc_con,
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apply homotopy_group_succ_in_con}
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