Theorems · Theorem · Lie groups

ContIntertwiningMap.smul_comp

∀ {R : Type u_1} {G : Type u_2} {V : Type u_3} {W : Type u_4} {U : Type u_5} [inst : Monoid G] [inst_1 : Ring R]
  [inst_2 : AddCommGroup V] [inst_3 : TopologicalSpace V] [inst_4 : IsTopologicalAddGroup V] [inst_5 : Module R V]
  [inst_6 : AddCommGroup W] [inst_7 : TopologicalSpace W] [inst_8 : IsTopologicalAddGroup W] [inst_9 : Module R W]
  [inst_10 : AddCommGroup U] [inst_11 : Module R U] [inst_12 : TopologicalSpace U] [inst_13 : IsTopologicalAddGroup U]
  {π₁ : ContRepresentation R G V} {π₂ : ContRepresentation R G W} {π₃ : ContRepresentation R G U} {S : Type u_7}
  [inst_14 : Monoid S] [inst_15 : DistribMulAction S U] [inst_16 : SMulCommClass R S U]
  [inst_17 : ContinuousConstSMul S U] [inst_18 : LinearMap.CompatibleSMul U U S R] (s : S)
  (f : ContIntertwiningMap π₂ π₃) (g : ContIntertwiningMap π₁ π₂), (s • f).comp g = s • f.comp g

Defined in

Mathlib.RepresentationTheory.Continuous.Basic

Cited by

1 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MonoidRingAddCommGroupTopologicalSpaceIsTopologicalAddGroupModuleAddCommGroupTopologicalSpaceIsTopologicalAddGroupModuleAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupMonoidDistribMulActionSMulCommClassContinuousConstSMulLinearMap.CompatibleSMul