Section Companion.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone2 gf.
Inductive cpn2 (r: rel) x0 x1 : Prop :=
| cpn2_intro
clo
(COM: compatible2 gf clo)
(CLO: clo r x0 x1)
.

Lemma cpn2_clo
r clo (LE: clo <3= cpn2):
clo (cpn2 r) <2= cpn2 r.