Section Main.
Variable gf: rel -> rel.
Hypothesis gf_mon: monotone13 gf.
Variant gpaco13 clo r rg x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 : Prop :=
| gpaco13_intro (IN: @rclo13 clo (paco13 (compose gf (rclo13 clo)) (rg \13/ r) \13/ r) x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12)
.
Definition gupaco13 clo r := gpaco13 clo r r.
Hint Resolve gpaco13_def_mon : paco.

Lemma gpaco13_mon clo r r' rg rg' x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12
(IN: @gpaco13 clo r rg x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12)
(LEr: r <13= r')
(LErg: rg <13= rg'):
@gpaco13 clo r' rg' x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12.