Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone10 gf.
Structure compatible10 (clo: rel -> rel) : Prop :=
compat10_intro {
compat10_mon: monotone10 clo;
compat10_compat : forall r,
clo (gf r) <10= gf (clo r);
}.
Structure wcompatible10 clo : Prop :=
wcompat10_intro {
wcompat10_mon: monotone10 clo;
wcompat10_wcompat : forall r,
clo (gf r) <10= gf (gupaco10 gf clo r);
}.

Lemma rclo10_dist clo
(MON: monotone10 clo)
(DIST: forall r1 r2, clo (r1 \10/ r2) <10= (clo r1 \10/ clo r2)):
forall r1 r2, rclo10 clo (r1 \10/ r2) <10= (rclo10 clo r1 \10/ rclo10 clo r2).