proposition: Lemma indom_update_inv : forall A `{Inhab B} (m:map A B) (i j:A) (v:B), j \indom (m[i:=v]) -> (j = i \/ j \indom m).
proof: Proof. Proof using. introv IB H. rewrite~ indom_update_eq in H. Qed.
imports: TLC(LibTactics LibLogic LibReflect LibOption LibRelation LibLogic LibOperation LibEpsilon LibMonoid LibSet)