From 091fd832586627fbf31375fb5487d5e6fa6f7053 Mon Sep 17 00:00:00 2001
From: Hannes Schulze <haschu0103@outlook.de>
Date: Sun, 26 Oct 2025 13:26:57 +0100
Subject: finish name abstraction 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 1726ed7..a2f8d56 100644
--- a/Nominal/Permutations.lean
+++ b/Nominal/Permutations.lean
@@ -138,6 +138,11 @@ lemma swap_mul_self {a b : X} : ⸨a, b⸩ * ⸨a, b⸩ = 1 := by
   apply ext
   simp [swap]
 
+/-- Lifting of Equiv.swap_comm to finite permutations. -/
+lemma swap_comm {a b : X} : ⸨a, b⸩ = ⸨b, a⸩ := by
+  apply ext
+  simp [swap, Equiv.swap_comm]
+
 /-- Lifting of Equiv.swap_apply_of_ne_of_ne to finite permutations. -/
 lemma swap_apply_of_ne_of_ne {a b c : X} : c ≠ a → c ≠ b → ⸨a, b⸩ c = c := by
   intro ha hb
-- 
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