Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone7 gf.
Structure compatible7 (clo: rel -> rel) : Prop :=
compat7_intro {
compat7_mon: monotone7 clo;
compat7_compat : forall r,
clo (gf r) <7= gf (clo r);
}.
Structure wcompatible7 clo : Prop :=
wcompat7_intro {
wcompat7_mon: monotone7 clo;
wcompat7_wcompat : forall r,
clo (gf r) <7= gf (gupaco7 gf clo r);
}.

Lemma rclo7_dist clo
(MON: monotone7 clo)
(DIST: forall r1 r2, clo (r1 \7/ r2) <7= (clo r1 \7/ clo r2)):
forall r1 r2, rclo7 clo (r1 \7/ r2) <7= (rclo7 clo r1 \7/ rclo7 clo r2).