proposition: Lemma _paco_convert_rev3: forall T0 T1 T2 (paco3: forall (y0: @T0) (y1: @T1 y0) (y2: @T2 y0 y1) , Prop) y0 y1 y2 x0 x1 x2 (EQ: _paco_id (@exist3T T0 T1 T2 x0 x1 x2 = @exist3T T0 T1 T2 y0 y1 y2)) (PACO: @paco3 y0 y1 y2), @paco3 x0 x1 x2.
proof: Proof. intros. apply (@f_equal (@sig3T T0 T1 T2) _ (fun x => @paco3 x.(proj3T0) x.(proj3T1) x.(proj3T2) )) in EQ. simpl in EQ. rewrite EQ. apply PACO. Qed.