Theorems · Theorem · linear algebra

LinearMap.map_coprod_prod

∀ {R : Type u} {M : Type v} {M₂ : Type w} {M₃ : Type y} [inst : Semiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : AddCommMonoid M₂] [inst_3 : AddCommMonoid M₃] [inst_4 : Module R M] [inst_5 : Module R M₂]
  [inst_6 : Module R M₃] (f : M →ₗ[R] M₃) (g : M₂ →ₗ[R] M₃) (p : Submodule R M) (q : Submodule R M₂),
  Submodule.map (f.coprod g) (p.prod q) = Submodule.map f p ⊔ Submodule.map g q

Defined in

Mathlib.LinearAlgebra.Prod

Cited by

1 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModule