Theorems · Theorem · linear algebra

LinearMap.comp_coprod

∀ {R : Type u} {M : Type v} {M₂ : Type w} {M₃ : Type y} {M₄ : Type z} [inst : Semiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : AddCommMonoid M₂] [inst_3 : AddCommMonoid M₃] [inst_4 : AddCommMonoid M₄] [inst_5 : Module R M]
  [inst_6 : Module R M₂] [inst_7 : Module R M₃] [inst_8 : Module R M₄] (f : M₃ →ₗ[R] M₄) (g₁ : M →ₗ[R] M₃)
  (g₂ : M₂ →ₗ[R] M₃), f ∘ₗ g₁.coprod g₂ = (f ∘ₗ g₁).coprod (f ∘ₗ g₂)

Defined in

Mathlib.LinearAlgebra.Prod

Cited by

2 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Quot.sound

Assumes

SemiringAddCommMonoidAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleModule