Section Main.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone4 gf.
Variant gpaco4 clo r rg x0 x1 x2 x3 : Prop :=
| gpaco4_intro (IN: @rclo4 clo (paco4 (compose gf (rclo4 clo)) (rg \4/ r) \4/ r) x0 x1 x2 x3)
.
Definition gupaco4 clo r := gpaco4 clo r r.
Hint Resolve gpaco4_def_mon : paco.

Lemma gpaco4_gpaco clo r rg:
gpaco4 clo (gpaco4 clo r rg) (gupaco4 clo (rg \4/ r)) <4= gpaco4 clo r rg.