Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone9 gf.
Structure compatible9 (clo: rel -> rel) : Prop :=
compat9_intro {
compat9_mon: monotone9 clo;
compat9_compat : forall r,
clo (gf r) <9= gf (clo r);
}.
Structure wcompatible9 clo : Prop :=
wcompat9_intro {
wcompat9_mon: monotone9 clo;
wcompat9_wcompat : forall r,
clo (gf r) <9= gf (gupaco9 gf clo r);
}.

Lemma rclo9_dist clo
(MON: monotone9 clo)
(DIST: forall r1 r2, clo (r1 \9/ r2) <9= (clo r1 \9/ clo r2)):
forall r1 r2, rclo9 clo (r1 \9/ r2) <9= (rclo9 clo r1 \9/ rclo9 clo r2).