Definition monotone3 T0 T1 T2 (gf: rel3 T0 T1 T2 -> rel3 T0 T1 T2) :=
  forall x0 x1 x2 r r' (IN: gf r x0 x1 x2) (LE: r <3= r'), gf r' x0 x1 x2.

(* Specifications: *)
Theorem paco3_acc: forall l r (OBG: forall rr (INC: r <3= rr) (CIH: l <_paco_3= rr), l <_paco_3= paco3 gf rr), l <3= paco3 gf r.
Theorem paco3_mon: monotone3 (paco3 gf).
Theorem paco3_mult_strong: forall r, paco3 gf (upaco3 gf r) <3= paco3 gf r.