Notation "\big [ op / idx ]_ ( i < n ) F" :=
  (\big[op/idx]_(i : ordinal n) F) : big_scope.Local Notation "x + y" := (plus x y).Notation "\max_ ( i 'in' A ) F" :=
 (\big[maxn/0%N]_(i in A) F%N) : nat_scope.

Lemma eq_big_nat m n F1 F2 : (forall i, m <= i < n -> F1 i = F2 i) -> \big[op/idx]_(m <= i < n) F1 i = \big[op/idx]_(m <= i < n) F2 i.