Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone5 gf.
Structure compatible5 (clo: rel -> rel) : Prop :=
compat5_intro {
compat5_mon: monotone5 clo;
compat5_compat : forall r,
clo (gf r) <5= gf (clo r);
}.
Structure wcompatible5 clo : Prop :=
wcompat5_intro {
wcompat5_mon: monotone5 clo;
wcompat5_wcompat : forall r,
clo (gf r) <5= gf (gupaco5 gf clo r);
}.

Lemma rclo5_dist clo
(MON: monotone5 clo)
(DIST: forall r1 r2, clo (r1 \5/ r2) <5= (clo r1 \5/ clo r2)):
forall r1 r2, rclo5 clo (r1 \5/ r2) <5= (rclo5 clo r1 \5/ rclo5 clo r2).