proposition: Theorem iff_push_down_impliesT : forall P Q R, (R -> (P <=> Q)) -> ((R -> P) <=> (R -> Q)).
proof: Proof. introv Hiff. repeat split; intros; apply Hiff; auto. Qed.
imports: Coq.Init.Notations tactics Peano Basics Bool Arith Arith.EqNat Omega