Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone8 gf.
Structure compatible8 (clo: rel -> rel) : Prop :=
compat8_intro {
compat8_mon: monotone8 clo;
compat8_compat : forall r,
clo (gf r) <8= gf (clo r);
}.
Structure wcompatible8 clo : Prop :=
wcompat8_intro {
wcompat8_mon: monotone8 clo;
wcompat8_wcompat : forall r,
clo (gf r) <8= gf (gupaco8 gf clo r);
}.

Lemma wcompat8_union clo1 clo2
(WCMP1: wcompatible8 clo1)
(WCMP2: wcompatible8 clo2):
wcompatible8 (clo1 \9/ clo2).