Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone12 gf.
Structure compatible12 (clo: rel -> rel) : Prop :=
compat12_intro {
compat12_mon: monotone12 clo;
compat12_compat : forall r,
clo (gf r) <12= gf (clo r);
}.
Structure wcompatible12 clo : Prop :=
wcompat12_intro {
wcompat12_mon: monotone12 clo;
wcompat12_wcompat : forall r,
clo (gf r) <12= gf (gupaco12 gf clo r);
}.

Lemma rclo12_dist clo
(MON: monotone12 clo)
(DIST: forall r1 r2, clo (r1 \12/ r2) <12= (clo r1 \12/ clo r2)):
forall r1 r2, rclo12 clo (r1 \12/ r2) <12= (rclo12 clo r1 \12/ rclo12 clo r2).