Theorems · Theorem · functional analysis

ContinuousLinearMap.comp_coprod

∀ {R : Type u_1} {M : Type u_3} {N : Type u_4} {M₁ : Type u_5} {M₂ : Type u_6} [inst : Semiring R]
  [inst_1 : TopologicalSpace M] [inst_2 : TopologicalSpace N] [inst_3 : TopologicalSpace M₁]
  [inst_4 : TopologicalSpace M₂] [inst_5 : AddCommMonoid M] [inst_6 : Module R M] [inst_7 : ContinuousAdd M]
  [inst_8 : AddCommMonoid N] [inst_9 : Module R N] [inst_10 : ContinuousAdd N] [inst_11 : AddCommMonoid M₁]
  [inst_12 : Module R M₁] [inst_13 : AddCommMonoid M₂] [inst_14 : Module R M₂] (f : M →L[R] N) (g₁ : M₁ →L[R] M)
  (g₂ : M₂ →L[R] M), f ∘SL g₁.coprod g₂ = (f ∘SL g₁).coprod (f ∘SL g₂)

Defined in

Mathlib.Topology.Algebra.Module.ContinuousLinearMap.PiProd

Cited by

1 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringTopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceAddCommMonoidModuleContinuousAddAddCommMonoidModuleContinuousAddAddCommMonoidModuleAddCommMonoidModule