Section Companion.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone0 gf.
Inductive cpn0 (r: rel) : Prop :=
| cpn0_intro
clo
(COM: compatible0 gf clo)
(CLO: clo r)
.

Lemma cpn0_clo
r clo (LE: clo <1= cpn0):
clo (cpn0 r) <0= cpn0 r.