proposition: Lemma PermutationA_app_comm l₁ l₂ : PermutationA (l₁ ++ l₂) (l₂ ++ l₁).
proof: Proof. induction l₁. now rewrite app_nil_r. rewrite <-app_comm_cons, IHl₁. now rewrite app_comm_cons, PermutationA_cons_append, <-app_assoc. Qed.
imports: Coq.Lists.List Coq.Lists.SetoidList MathClasses.interfaces.abstract_algebra MathClasses.interfaces.monads MathClasses.theory.monads