Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone7 gf.
Structure compatible7 (clo: rel -> rel) : Prop :=
compat7_intro {
compat7_mon: monotone7 clo;
compat7_compat : forall r,
clo (gf r) <7= gf (clo r);
}.
Structure wcompatible7 clo : Prop :=
wcompat7_intro {
wcompat7_mon: monotone7 clo;
wcompat7_wcompat : forall r,
clo (gf r) <7= gf (gupaco7 gf clo r);
}.

Lemma wcompat7_union clo1 clo2
(WCMP1: wcompatible7 clo1)
(WCMP2: wcompatible7 clo2):
wcompatible7 (clo1 \8/ clo2).