[Merged by Bors] - chore(group_theory/perm): Add alternate formulation of (sum|sigma)_congr lemmas #5260
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…ngr lemmas These lemmas existed already for `equiv`, but not for `perm` or for `perm` via group structures.
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Co-authored-by: Bryan Gin-ge Chen <bryangingechen@gmail.com>
This was referenced Dec 7, 2020
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…ngr lemmas (#5260) These lemmas existed already for `equiv`, but not for `perm` or for `perm` via group structures.
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| @[simp] lemma sigma_congr_right_mul {α} {β : α → Type*} | ||
| (F : Π a, perm (β a)) (G : Π a, perm (β a)) : | ||
| sigma_congr_right F * sigma_congr_right G = sigma_congr_right (λ a, F a * G a) := | ||
| sigma_congr_right_trans G F | ||
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| @[simp] lemma sigma_congr_right_inv {α} {β : α → Type*} (F : Π a, perm (β a)) : | ||
| (sigma_congr_right F)⁻¹ = sigma_congr_right (λ a, (F a)⁻¹) := | ||
| sigma_congr_right_symm F | ||
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| @[simp] lemma sigma_congr_right_one {α} {β : α → Type*} : | ||
| (sigma_congr_right (λ a, (1 : equiv.perm $ β a))) = 1 := | ||
| sigma_congr_right_refl |
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Once #5280 is in, I can remove these lemmas and replace them in a follow-up PR with
def sigma_congr_right_hom {α} {β : α → Type*} : Π a, perm (β a) →* perm (Σ a, β a) :=
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Pull request successfully merged into master. Build succeeded: |
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These lemmas existed already for
equiv, but not forpermor forpermvia group structures.