Section Main.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone12 gf.
Variant gpaco12 clo r rg x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : Prop :=
| gpaco12_intro (IN: @rclo12 clo (paco12 (compose gf (rclo12 clo)) (rg \12/ r) \12/ r) x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11)
.
Definition gupaco12 clo r := gpaco12 clo r r.
Hint Resolve gpaco12_def_mon : paco.

Lemma gpaco12_mon clo r r' rg rg' x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11
(IN: @gpaco12 clo r rg x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11)
(LEr: r <12= r')
(LErg: rg <12= rg'):
@gpaco12 clo r' rg' x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11.