Section Compatibility.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone6 gf.
Structure compatible6 (clo: rel -> rel) : Prop :=
compat6_intro {
compat6_mon: monotone6 clo;
compat6_compat : forall r,
clo (gf r) <6= gf (clo r);
}.
Structure wcompatible6 clo : Prop :=
wcompat6_intro {
wcompat6_mon: monotone6 clo;
wcompat6_wcompat : forall r,
clo (gf r) <6= gf (gupaco6 gf clo r);
}.

Lemma rclo6_dist clo
(MON: monotone6 clo)
(DIST: forall r1 r2, clo (r1 \6/ r2) <6= (clo r1 \6/ clo r2)):
forall r1 r2, rclo6 clo (r1 \6/ r2) <6= (rclo6 clo r1 \6/ rclo6 clo r2).