Section Main.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone2 gf.
Variant gpaco2 clo r rg x0 x1 : Prop :=
| gpaco2_intro (IN: @rclo2 clo (paco2 (compose gf (rclo2 clo)) (rg \2/ r) \2/ r) x0 x1)
.
Definition gupaco2 clo r := gpaco2 clo r r.
Hint Resolve gpaco2_def_mon : paco.

Lemma gpaco2_weaken  clo r rg:
gpaco2 (gupaco2 clo) r rg <2= gpaco2 clo r rg.