Section RClo.
Inductive rclo8 (clo: rel->rel) (r: rel): rel :=
| rclo8_base
x0 x1 x2 x3 x4 x5 x6 x7
(IN: r x0 x1 x2 x3 x4 x5 x6 x7):
@rclo8 clo r x0 x1 x2 x3 x4 x5 x6 x7
| rclo8_clo'
r' x0 x1 x2 x3 x4 x5 x6 x7
(LE: r' <8= rclo8 clo r)
(IN: clo r' x0 x1 x2 x3 x4 x5 x6 x7):
@rclo8 clo r x0 x1 x2 x3 x4 x5 x6 x7
.

Lemma rclo8_compose clo r:
rclo8 (rclo8 clo) r <8= rclo8 clo r.