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 wcompat6_compat clo
(WCMP: wcompatible6 clo) :
compatible6 (gupaco6 gf clo).