Section Companion.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone3 gf.
Inductive cpn3 (r: rel) x0 x1 x2 : Prop :=
| cpn3_intro
clo
(COM: compatible3 gf clo)
(CLO: clo r x0 x1 x2)
.

Lemma cpn3_clo
r clo (LE: clo <4= cpn3):
clo (cpn3 r) <3= cpn3 r.