Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone12 gf.
Structure compatible12 (clo: rel -> rel) : Prop :=
compat12_intro {
compat12_mon: monotone12 clo;
compat12_compat : forall r,
clo (gf r) <12= gf (clo r);
}.
Structure wcompatible12 clo : Prop :=
wcompat12_intro {
wcompat12_mon: monotone12 clo;
wcompat12_wcompat : forall r,
clo (gf r) <12= gf (gupaco12 gf clo r);
}.

Lemma wcompat12_union clo1 clo2
(WCMP1: wcompatible12 clo1)
(WCMP2: wcompatible12 clo2):
wcompatible12 (clo1 \13/ clo2).