Definition monotone4 T0 T1 T2 T3 (gf: rel4 T0 T1 T2 T3 -> rel4 T0 T1 T2 T3) :=
  forall x0 x1 x2 x3 r r' (IN: gf r x0 x1 x2 x3) (LE: r <4= r'), gf r' x0 x1 x2 x3.

(* Specifications: *)
Theorem paco4_acc: forall l r (OBG: forall rr (INC: r <4= rr) (CIH: l <_paco_4= rr), l <_paco_4= paco4 gf rr), l <4= paco4 gf r.
Theorem paco4_mon: monotone4 (paco4 gf).
Theorem paco4_mult_strong: forall r, paco4 gf (upaco4 gf r) <4= paco4 gf r.