Section GeneralMonotonicity.
Variable gf: rel -> rel.

Lemma gpaco12_mon_bot (gf' clo clo': rel -> rel) x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 r' rg'
(IN: @gpaco12 gf clo bot12 bot12 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11)
(gf_mon: monotone12 gf)
(LEgf: gf <13= gf')
(LEclo: clo <13= clo'):
@gpaco12 gf' clo' r' rg' x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11.