Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone2 gf.
Structure compatible2 (clo: rel -> rel) : Prop :=
compat2_intro {
compat2_mon: monotone2 clo;
compat2_compat : forall r,
clo (gf r) <2= gf (clo r);
}.
Structure wcompatible2 clo : Prop :=
wcompat2_intro {
wcompat2_mon: monotone2 clo;
wcompat2_wcompat : forall r,
clo (gf r) <2= gf (gupaco2 gf clo r);
}.

Lemma rclo2_dist clo
(MON: monotone2 clo)
(DIST: forall r1 r2, clo (r1 \2/ r2) <2= (clo r1 \2/ clo r2)):
forall r1 r2, rclo2 clo (r1 \2/ r2) <2= (rclo2 clo r1 \2/ rclo2 clo r2).