Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone3 gf.
Structure compatible3 (clo: rel -> rel) : Prop :=
compat3_intro {
compat3_mon: monotone3 clo;
compat3_compat : forall r,
clo (gf r) <3= gf (clo r);
}.
Structure wcompatible3 clo : Prop :=
wcompat3_intro {
wcompat3_mon: monotone3 clo;
wcompat3_wcompat : forall r,
clo (gf r) <3= gf (gupaco3 gf clo r);
}.

Lemma rclo3_dist clo
(MON: monotone3 clo)
(DIST: forall r1 r2, clo (r1 \3/ r2) <3= (clo r1 \3/ clo r2)):
forall r1 r2, rclo3 clo (r1 \3/ r2) <3= (rclo3 clo r1 \3/ rclo3 clo r2).