Definition monotone2 T0 T1 (gf: rel2 T0 T1 -> rel2 T0 T1) :=
  forall x0 x1 r r' (IN: gf r x0 x1) (LE: r <2= r'), gf r' x0 x1.

(* Specifications: *)
Theorem paco2_acc: forall l r (OBG: forall rr (INC: r <2= rr) (CIH: l <_paco_2= rr), l <_paco_2= paco2 gf rr), l <2= paco2 gf r.
Theorem paco2_mon: monotone2 (paco2 gf).
Theorem paco2_mult_strong: forall r, paco2 gf (upaco2 gf r) <2= paco2 gf r.