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Diffstat (limited to 'Nominal/Permutations.lean')
| -rw-r--r-- | Nominal/Permutations.lean | 10 |
1 files changed, 10 insertions, 0 deletions
diff --git a/Nominal/Permutations.lean b/Nominal/Permutations.lean index 4a3e88f..1bcb00f 100644 --- a/Nominal/Permutations.lean +++ b/Nominal/Permutations.lean @@ -116,6 +116,11 @@ end Equiv.Perm namespace FPerm +/-- Extensionality lemma for finite permutations. -/ +lemma ext {X : Type} {π₁ π₂ : FPerm X} : π₁.val = π₂.val → π₁ = π₂ := by + intro h; ext; rw [h] + +/-- Transpositions are finite permutations. -/ def swap (x y : X) : FPerm X := ⟨Equiv.swap x y, by apply Set.Finite.subset · apply ({x, y} : Finset X).finite_toSet @@ -123,6 +128,11 @@ def swap (x y : X) : FPerm X := ⟨Equiv.swap x y, by notation "⸨" a "," b "⸩" => FPerm.swap a b +/-- Lifting of Equiv.mul_swap_eq_swap_mul to finite permutations. -/ +lemma mul_swap_eq_swap_mul {π : FPerm X} {a b : X} : π * ⸨a, b⸩ = ⸨π a, π b⸩ * π := by + apply ext + apply Equiv.mul_swap_eq_swap_mul + end FPerm example : FPerm ℕ := ⸨1, 2⸩ * ⸨3, 4⸩ * ⸨2, 3⸩ |