Section RClo.
Inductive rclo9 (clo: rel->rel) (r: rel): rel :=
| rclo9_base
x0 x1 x2 x3 x4 x5 x6 x7 x8
(IN: r x0 x1 x2 x3 x4 x5 x6 x7 x8):
@rclo9 clo r x0 x1 x2 x3 x4 x5 x6 x7 x8
| rclo9_clo'
r' x0 x1 x2 x3 x4 x5 x6 x7 x8
(LE: r' <9= rclo9 clo r)
(IN: clo r' x0 x1 x2 x3 x4 x5 x6 x7 x8):
@rclo9 clo r x0 x1 x2 x3 x4 x5 x6 x7 x8
.

Lemma rclo9_rclo clo r:
rclo9 clo (rclo9 clo r) <9= rclo9 clo r.