proposition: Lemma big_nat_cond m n (P : pred nat) F : \big[op/idx]_(m <= i < n | P i) F i = \big[op/idx]_(m <= i < n | (m <= i < n) && P i) F i.
proof: Proof. by rewrite big_seq_cond; apply: eq_bigl => i; rewrite mem_index_iota. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div fintype tuple finfun)