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_greatest: forall clo (COM: compatible3 gf clo), clo <4= cpn3.