Definition monotone1 T0 (gf: rel1 T0 -> rel1 T0) :=
  forall x0 r r' (IN: gf r x0) (LE: r <1= r'), gf r' x0.

(* Specifications: *)
Theorem paco1_acc: forall l r (OBG: forall rr (INC: r <1= rr) (CIH: l <_paco_1= rr), l <_paco_1= paco1 gf rr), l <1= paco1 gf r.
Theorem paco1_mon: monotone1 (paco1 gf).
Theorem paco1_mult_strong: forall r, paco1 gf (upaco1 gf r) <1= paco1 gf r.