Section BigConst.
Variables (R : Type) (idx : R) (op : R -> R -> R).

Lemma big_nat_widenl (m1 m2 n : nat) (P : pred nat) F :
m2 <= m1 ->
\big[op/idx]_(m1 <= i < n | P i) F i =
\big[op/idx]_(m2 <= i < n | P i && (m1 <= i)) F i.