Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone11 gf.
Structure compatible11 (clo: rel -> rel) : Prop :=
compat11_intro {
compat11_mon: monotone11 clo;
compat11_compat : forall r,
clo (gf r) <11= gf (clo r);
}.
Structure wcompatible11 clo : Prop :=
wcompat11_intro {
wcompat11_mon: monotone11 clo;
wcompat11_wcompat : forall r,
clo (gf r) <11= gf (gupaco11 gf clo r);
}.

Lemma rclo11_dist clo
(MON: monotone11 clo)
(DIST: forall r1 r2, clo (r1 \11/ r2) <11= (clo r1 \11/ clo r2)):
forall r1 r2, rclo11 clo (r1 \11/ r2) <11= (rclo11 clo r1 \11/ rclo11 clo r2).