Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone5 gf.
Structure compatible5 (clo: rel -> rel) : Prop :=
compat5_intro {
compat5_mon: monotone5 clo;
compat5_compat : forall r,
clo (gf r) <5= gf (clo r);
}.
Structure wcompatible5 clo : Prop :=
wcompat5_intro {
wcompat5_mon: monotone5 clo;
wcompat5_wcompat : forall r,
clo (gf r) <5= gf (gupaco5 gf clo r);
}.

Lemma wcompat5_compat clo
(WCMP: wcompatible5 clo) :
compatible5 (gupaco5 gf clo).