Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone1 gf.
Structure compatible1 (clo: rel -> rel) : Prop :=
compat1_intro {
compat1_mon: monotone1 clo;
compat1_compat : forall r,
clo (gf r) <1= gf (clo r);
}.
Structure wcompatible1 clo : Prop :=
wcompat1_intro {
wcompat1_mon: monotone1 clo;
wcompat1_wcompat : forall r,
clo (gf r) <1= gf (gupaco1 gf clo r);
}.

Lemma rclo1_dist clo
(MON: monotone1 clo)
(DIST: forall r1 r2, clo (r1 \1/ r2) <1= (clo r1 \1/ clo r2)):
forall r1 r2, rclo1 clo (r1 \1/ r2) <1= (rclo1 clo r1 \1/ rclo1 clo r2).