Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone4 gf.
Structure compatible4 (clo: rel -> rel) : Prop :=
compat4_intro {
compat4_mon: monotone4 clo;
compat4_compat : forall r,
clo (gf r) <4= gf (clo r);
}.
Structure wcompatible4 clo : Prop :=
wcompat4_intro {
wcompat4_mon: monotone4 clo;
wcompat4_wcompat : forall r,
clo (gf r) <4= gf (gupaco4 gf clo r);
}.

Lemma wcompat4_compat clo
(WCMP: wcompatible4 clo) :
compatible4 (gupaco4 gf clo).