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 rclo8_dist clo
(MON: monotone8 clo)
(DIST: forall r1 r2, clo (r1 \8/ r2) <8= (clo r1 \8/ clo r2)):
forall r1 r2, rclo8 clo (r1 \8/ r2) <8= (rclo8 clo r1 \8/ rclo8 clo r2).