Theorems · Theorem · linear algebra

MultilinearMap.map_sub_map_piecewise

∀ {R : Type uR} {ι : Type uι} {M₁ : ι → Type v₁} {M₂ : Type v₂} [inst : Semiring R]
  [inst_1 : (i : ι) → AddCommGroup (M₁ i)] [inst_2 : AddCommGroup M₂] [inst_3 : (i : ι) → Module R (M₁ i)]
  [inst_4 : Module R M₂] (f : MultilinearMap R M₁ M₂) [inst_5 : LinearOrder ι] (a b : (i : ι) → M₁ i) (s : Finset ι),
  f a - f (s.piecewise b a) = ∑ i ∈ s, f fun j => if j ∈ s → j < i then a j else if i = j then a j - b j else b j

Defined in

Mathlib.LinearAlgebra.Multilinear.Basic

Cited by

1 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommGroupAddCommGroupModuleModuleLinearOrder