Theorems · Theorem · functional analysis

ContinuousLinearMap.coprod_add

∀ {R : Type u_1} {M : Type u_3} {M₁ : Type u_5} {M₂ : Type u_6} [inst : Semiring R] [inst_1 : TopologicalSpace M]
  [inst_2 : TopologicalSpace M₁] [inst_3 : TopologicalSpace M₂] [inst_4 : AddCommMonoid M] [inst_5 : Module R M]
  [inst_6 : ContinuousAdd M] [inst_7 : AddCommMonoid M₁] [inst_8 : Module R M₁] [inst_9 : AddCommMonoid M₂]
  [inst_10 : Module R M₂] (f₁ g₁ : M₁ →L[R] M) (f₂ g₂ : M₂ →L[R] M),
  (f₁ + g₁).coprod (f₂ + g₂) = f₁.coprod f₂ + g₁.coprod g₂

Defined in

Mathlib.Topology.Algebra.Module.ContinuousLinearMap.PiProd

Cited by

0 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringTopologicalSpaceTopologicalSpaceTopologicalSpaceAddCommMonoidModuleContinuousAddAddCommMonoidModuleAddCommMonoidModule