Section FCI.
Variables (X: eqType) (sigma: list X -> X -> bool) (R: list X).
Definition F (A : list X) : list X.
destruct (pick A) as [[x _]|_].
- exact (x::A).
- exact A.
Defined.
Definition C := it F (card R) nil.

Lemma ind p :
(forall A x, inclp A p -> x el R -> sigma A x -> p x) -> inclp C p.