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_filter_cond r (P1 P2 : pred I) F : \big[op/idx]_(i <- filter P1 r | P2 i) F i = \big[op/idx]_(i <- r | P1 i && P2 i) F i.