Theorems · Theorem · functional analysis

ContinuousLinearMap.coprod_comp_inl_inr

∀ {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]
  [ContinuousAdd M] [inst_7 : AddCommMonoid M₁] [inst_8 : Module R M₁] [inst_9 : AddCommMonoid M₂]
  [inst_10 : Module R M₂] [ContinuousAdd M₁] [inst_12 : ContinuousAdd M₂] (f : M × M₁ →L[R] M₂),
  (f ∘SL ContinuousLinearMap.inl R M M₁).coprod (f ∘SL ContinuousLinearMap.inr R M M₁) = f

Defined in

Mathlib.Topology.Algebra.Module.ContinuousLinearMap.PiProd

Cited by

1 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringTopologicalSpaceTopologicalSpaceTopologicalSpaceAddCommMonoidModuleContinuousAddAddCommMonoidModuleAddCommMonoidModuleContinuousAddContinuousAdd