Section Companion.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone9 gf.
Inductive cpn9 (r: rel) x0 x1 x2 x3 x4 x5 x6 x7 x8 : Prop :=
| cpn9_intro
clo
(COM: compatible9 gf clo)
(CLO: clo r x0 x1 x2 x3 x4 x5 x6 x7 x8)
.

Lemma cpn9_clo
r clo (LE: clo <10= cpn9):
clo (cpn9 r) <9= cpn9 r.