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_clo
r clo (LE: clo <2= cpn1):
clo (cpn1 r) <1= cpn1 r.