Section Companion.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone4 gf.
Inductive cpn4 (r: rel) x0 x1 x2 x3 : Prop :=
| cpn4_intro
clo
(COM: compatible4 gf clo)
(CLO: clo r x0 x1 x2 x3)
.

Lemma cpn4_clo
r clo (LE: clo <5= cpn4):
clo (cpn4 r) <4= cpn4 r.