Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone9 gf.
Structure compatible9 (clo: rel -> rel) : Prop :=
compat9_intro {
compat9_mon: monotone9 clo;
compat9_compat : forall r,
clo (gf r) <9= gf (clo r);
}.
Structure wcompatible9 clo : Prop :=
wcompat9_intro {
wcompat9_mon: monotone9 clo;
wcompat9_wcompat : forall r,
clo (gf r) <9= gf (gupaco9 gf clo r);
}.

Lemma wcompat9_compat clo
(WCMP: wcompatible9 clo) :
compatible9 (gupaco9 gf clo).