Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone13 gf.
Structure compatible13 (clo: rel -> rel) : Prop :=
compat13_intro {
compat13_mon: monotone13 clo;
compat13_compat : forall r,
clo (gf r) <13= gf (clo r);
}.
Structure wcompatible13 clo : Prop :=
wcompat13_intro {
wcompat13_mon: monotone13 clo;
wcompat13_wcompat : forall r,
clo (gf r) <13= gf (gupaco13 gf clo r);
}.

Lemma rclo13_dist clo
(MON: monotone13 clo)
(DIST: forall r1 r2, clo (r1 \13/ r2) <13= (clo r1 \13/ clo r2)):
forall r1 r2, rclo13 clo (r1 \13/ r2) <13= (rclo13 clo r1 \13/ rclo13 clo r2).