Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone4 gf.
Structure compatible4 (clo: rel -> rel) : Prop :=
compat4_intro {
compat4_mon: monotone4 clo;
compat4_compat : forall r,
clo (gf r) <4= gf (clo r);
}.
Structure wcompatible4 clo : Prop :=
wcompat4_intro {
wcompat4_mon: monotone4 clo;
wcompat4_wcompat : forall r,
clo (gf r) <4= gf (gupaco4 gf clo r);
}.

Lemma rclo4_dist clo
(MON: monotone4 clo)
(DIST: forall r1 r2, clo (r1 \4/ r2) <4= (clo r1 \4/ clo r2)):
forall r1 r2, rclo4 clo (r1 \4/ r2) <4= (rclo4 clo r1 \4/ rclo4 clo r2).