Section Main.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone1 gf.
Variant gpaco1 clo r rg x0 : Prop :=
| gpaco1_intro (IN: @rclo1 clo (paco1 (compose gf (rclo1 clo)) (rg \1/ r) \1/ r) x0)
.
Definition gupaco1 clo r := gpaco1 clo r r.
Hint Resolve gpaco1_def_mon : paco.

Lemma gpaco1_gpaco clo r rg:
gpaco1 clo (gpaco1 clo r rg) (gupaco1 clo (rg \1/ r)) <1= gpaco1 clo r rg.