Section Main.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone3 gf.
Variant gpaco3 clo r rg x0 x1 x2 : Prop :=
| gpaco3_intro (IN: @rclo3 clo (paco3 (compose gf (rclo3 clo)) (rg \3/ r) \3/ r) x0 x1 x2)
.
Definition gupaco3 clo r := gpaco3 clo r r.
Hint Resolve gpaco3_def_mon : paco.

Lemma gpaco3_gpaco clo r rg:
gpaco3 clo (gpaco3 clo r rg) (gupaco3 clo (rg \3/ r)) <3= gpaco3 clo r rg.