Documentation

Mathlib.Data.Rat.BigOperators

Casting lemmas for rational numbers involving sums and products #

@[simp]
theorem Rat.cast_list_sum {α : Type u_2} [DivisionRing α] [CharZero α] (s : List ) :
s.sum = (List.map Rat.cast s).sum
@[simp]
theorem Rat.cast_multiset_sum {α : Type u_2} [DivisionRing α] [CharZero α] (s : Multiset ) :
s.sum = (Multiset.map Rat.cast s).sum
@[simp]
theorem Rat.cast_sum {ι : Type u_1} {α : Type u_2} [DivisionRing α] [CharZero α] (s : Finset ι) (f : ι) :
(∑ is, f i) = is, (f i)
@[simp]
theorem Rat.cast_list_prod {α : Type u_2} [DivisionRing α] [CharZero α] (s : List ) :
s.prod = (List.map Rat.cast s).prod
@[simp]
theorem Rat.cast_multiset_prod {α : Type u_2} [Field α] [CharZero α] (s : Multiset ) :
s.prod = (Multiset.map Rat.cast s).prod
@[simp]
theorem Rat.cast_prod {ι : Type u_1} {α : Type u_2} [Field α] [CharZero α] (s : Finset ι) (f : ι) :
(∏ is, f i) = is, (f i)