Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone0 gf.
Structure compatible0 (clo: rel -> rel) : Prop :=
compat0_intro {
compat0_mon: monotone0 clo;
compat0_compat : forall r,
clo (gf r) <0= gf (clo r);
}.
Structure wcompatible0 clo : Prop :=
wcompat0_intro {
wcompat0_mon: monotone0 clo;
wcompat0_wcompat : forall r,
clo (gf r) <0= gf (gupaco0 gf clo r);
}.

Lemma rclo0_dist clo
(MON: monotone0 clo)
(DIST: forall r1 r2, clo (r1 \0/ r2) <0= (clo r1 \0/ clo r2)):
forall r1 r2, rclo0 clo (r1 \0/ r2) <0= (rclo0 clo r1 \0/ rclo0 clo r2).