From c3700706466cb8fb9ed287ea066b656caacdc9c7 Mon Sep 17 00:00:00 2001
From: Hannes Schulze <haschu0103@outlook.de>
Date: Sat, 25 Oct 2025 01:07:56 +0200
Subject: start working on alpha equivalence proofs

---
 Nominal/Permutations.lean | 5 +++++
 1 file changed, 5 insertions(+)

(limited to 'Nominal/Permutations.lean')

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
-- 
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