proposition: Lemma big_ltn_cond : forall m n (P : pred nat) F, m < n -> let x := \big[op/idx]_(m.+1 <= i < n | P i) F i in \big[op/idx]_(m <= i < n | P i) F i === if P m then op (F m) x else x.
proof: Proof. move=> m [//|n] P F le_m_n; rewrite /index_iota leq_subS //=. by case: (P m); reflexivity. Qed.
imports: ssreflect ssrbool ssrfun eqtype ssrnat seq div choice fintype finfun paths Setoid Morphisms OperationClasses bigops