Section Companion.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone9 gf.
Inductive cpn9 (r: rel) x0 x1 x2 x3 x4 x5 x6 x7 x8 : Prop :=
| cpn9_intro
clo
(COM: compatible9 gf clo)
(CLO: clo r x0 x1 x2 x3 x4 x5 x6 x7 x8)
.

Lemma cpn9_uclo uclo
(MON: monotone9 uclo)
(WCOM: forall r, uclo (gf r) <9= gf (gupaco9 gf (uclo \10/ cpn9) r)):
uclo <10= gupaco9 gf cpn9.