Section Companion.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone8 gf.
Inductive cpn8 (r: rel) x0 x1 x2 x3 x4 x5 x6 x7 : Prop :=
| cpn8_intro
clo
(COM: compatible8 gf clo)
(CLO: clo r x0 x1 x2 x3 x4 x5 x6 x7)
.

Lemma cpn8_clo
r clo (LE: clo <9= cpn8):
clo (cpn8 r) <8= cpn8 r.