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 big_ord_narrow n1 n2 F (le_n12 : n1 <= n2) : let w := widen_ord le_n12 in \big[op/idx]_(i < n2 | i < n1) F i = \big[op/idx]_(i < n1) F (w i).