fact: Definition Pick := \big[Or/False]_(p : {ffun pred I}) ((\big[And/True]_i (if p i then pred_f i else ~ pred_f i)) /\ (if pick p is Some i then then_f i else else_f))%T.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop prime binomial)