proposition: Lemma eq_union_restrict_remove : forall A (E:set A) B (M:map A B), M = (M \- E) \u (M \| E).
proof: Proof. Proof using. intros. applys fun_ext_1. intros k. simpls. unfolds remove_impl, restrict_impl, union_impl. case_if~. destruct~ (M k). Qed.
imports: TLC(LibTactics LibLogic LibReflect LibOption LibRelation LibLogic LibOperation LibEpsilon LibMonoid LibSet)