proposition: Theorem dont_touch_forall : forall (P Q : (nat : Set) -> [univ]), (forall (n : (nat : Set)), P n <=> (forall (m : (nat : Set)), Q (m+n))) -> P (1 : (nat : Set)) -> forall (m : (nat : Set)), Q (m+1).
proof: Proof. intros ? ? Hif Hp1. rw Hif in Hp1; trivial. Qed.
imports: universe Coq.Setoids.Setoid