Theorems · Theorem · linear algebra

LinearMap.sum_apply

∀ {R : Type u_1} {R₂ : Type u_3} {M : Type u_5} {M₂ : Type u_7} {ι : Type u_9} [inst : Semiring R]
  [inst_1 : Semiring R₂] [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M]
  [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂} (t : Finset ι) (f : ι → M →ₛₗ[σ₁₂] M₂) (b : M),
  (∑ d ∈ t, f d) b = ∑ d ∈ t, (f d) b

Defined in

Mathlib.Algebra.Module.Submodule.LinearMap

Cited by

14 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModule