proposition: Lemma remove_perm_single : forall x a b M, x / (rem a (rem b M)) = x / (rem b (rem a M)).
proof: Proof. intros x a b M. case (eqA_dec x a); case (eqA_dec x b); intros x_b x_a. rewrite !mult_remove_in; trivial. rewrite mult_remove_in; trivial. do 2 (rewrite mult_remove_not_in; trivial). rewrite mult_remove_in; trivial. rewrite mult_remove_not_in; trivial. do 2 (rewrite mult_remove_in; trivial). rewrite mult_remove_not_in; trivial. rewrite !mult_remove_not_in; trivial. Qed.
imports: Coq(Permutation PermutSetoid Lia Multiset) CoLoR(LogicUtil RelExtras MultisetCore ListExtras)