Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone13 gf.
Structure compatible13 (clo: rel -> rel) : Prop :=
compat13_intro {
compat13_mon: monotone13 clo;
compat13_compat : forall r,
clo (gf r) <13= gf (clo r);
}.
Structure wcompatible13 clo : Prop :=
wcompat13_intro {
wcompat13_mon: monotone13 clo;
wcompat13_wcompat : forall r,
clo (gf r) <13= gf (gupaco13 gf clo r);
}.

Lemma wcompat13_union clo1 clo2
(WCMP1: wcompatible13 clo1)
(WCMP2: wcompatible13 clo2):
wcompatible13 (clo1 \14/ clo2).