Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone10 gf.
Structure compatible10 (clo: rel -> rel) : Prop :=
compat10_intro {
compat10_mon: monotone10 clo;
compat10_compat : forall r,
clo (gf r) <10= gf (clo r);
}.
Structure wcompatible10 clo : Prop :=
wcompat10_intro {
wcompat10_mon: monotone10 clo;
wcompat10_wcompat : forall r,
clo (gf r) <10= gf (gupaco10 gf clo r);
}.

Lemma wcompat10_union clo1 clo2
(WCMP1: wcompatible10 clo1)
(WCMP2: wcompatible10 clo2):
wcompatible10 (clo1 \11/ clo2).