Section Companion.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone12 gf.
Inductive cpn12 (r: rel) x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : Prop :=
| cpn12_intro
clo
(COM: compatible12 gf clo)
(CLO: clo r x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11)
.

Lemma cpn12_clo
r clo (LE: clo <13= cpn12):
clo (cpn12 r) <12= cpn12 r.