proposition: Lemma demo_intros_all : (forall a b, P1 a -> P2 b -> IMP H1 a b) /\ (forall a b, a = 0 -> b = 1 -> ~ (a = b)).
proof: Proof. Proof using. split. intros_all. demo. intros_all. demo. Qed.
imports: TLC(LibTactics) Coq.micromega.Lia