Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone0 gf.
Structure compatible0 (clo: rel -> rel) : Prop :=
compat0_intro {
compat0_mon: monotone0 clo;
compat0_compat : forall r,
clo (gf r) <0= gf (clo r);
}.
Structure wcompatible0 clo : Prop :=
wcompat0_intro {
wcompat0_mon: monotone0 clo;
wcompat0_wcompat : forall r,
clo (gf r) <0= gf (gupaco0 gf clo r);
}.

Lemma wcompat0_union clo1 clo2
(WCMP1: wcompatible0 clo1)
(WCMP2: wcompatible0 clo2):
wcompatible0 (clo1 \1/ clo2).