proposition: Lemma demo_forwards_1 : forall x : nat, x > 1 -> (forall z, z > 1 -> exists y, z < 2 /\ z <> y) -> True.
proof: Proof. Proof using. introv Le H. dup 4. forwards Q: H. eauto. demo. forwards [y [R1 R2]]: H. eauto. demo. forwards: H. eauto. demo. forwards: Le. demo. Qed.
imports: TLC(LibTactics) Coq.micromega.Lia