proposition: Lemma diff_mult_step_eq : forall M N a x, x =A= a -> x / (rem a M - N) = ((x / (M - N))%msets - 1)%nat.
proof: Proof. intros M N a x x_a. rewrite diff_perm. rewrite mult_remove_in; trivial. Qed.
imports: Coq(Permutation PermutSetoid Lia Multiset) CoLoR(LogicUtil RelExtras MultisetCore ListExtras)