Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone11 gf.
Structure compatible11 (clo: rel -> rel) : Prop :=
compat11_intro {
compat11_mon: monotone11 clo;
compat11_compat : forall r,
clo (gf r) <11= gf (clo r);
}.
Structure wcompatible11 clo : Prop :=
wcompat11_intro {
wcompat11_mon: monotone11 clo;
wcompat11_wcompat : forall r,
clo (gf r) <11= gf (gupaco11 gf clo r);
}.

Lemma wcompat11_union clo1 clo2
(WCMP1: wcompatible11 clo1)
(WCMP2: wcompatible11 clo2):
wcompatible11 (clo1 \12/ clo2).