Section Companion.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone1 gf.
Inductive cpn1 (r: rel) x0 : Prop :=
| cpn1_intro
clo
(COM: compatible1 gf clo)
(CLO: clo r x0)
.

Lemma cpn1_uclo uclo
(MON: monotone1 uclo)
(WCOM: forall r, uclo (gf r) <1= gf (gupaco1 gf (uclo \2/ cpn1) r)):
uclo <2= gupaco1 gf cpn1.