proposition: Lemma big_nth x0 r (P : pred I) F : \big[op/idx]_(i <- r | P i) F i = \big[op/idx]_(0 <= i < size r | P (nth x0 r i)) (F (nth x0 r i)).
proof: Proof. by rewrite -[r in LHS](mkseq_nth x0) big_map /index_iota subn0. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div fintype tuple finfun)