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Diffstat (limited to 'Nominal/Permutations.lean')
| -rw-r--r-- | Nominal/Permutations.lean | 5 |
1 files changed, 5 insertions, 0 deletions
diff --git a/Nominal/Permutations.lean b/Nominal/Permutations.lean index b8d510e..62d7470 100644 --- a/Nominal/Permutations.lean +++ b/Nominal/Permutations.lean @@ -133,6 +133,11 @@ lemma mul_swap_eq_swap_mul {π : FPerm X} {a b : X} : π * ⸨a, b⸩ = ⸨π a, apply ext apply Equiv.mul_swap_eq_swap_mul +/-- Lifting of Equiv.swap_mul_self to finite permutations. -/ +lemma swap_mul_self {a b : X} : ⸨a, b⸩ * ⸨a, b⸩ = 1 := by + apply ext + simp [swap] + /-- If c is not equal to a or b, then (a b) leaves c unchanged. -/ lemma swap_neq {a b c : X} : c ≠ a → c ≠ b → ⸨a, b⸩ c = c := by intro ha hb |