Theorems · Theorem · order theory

PositiveLinearMap.map_smul_of_tower

∀ {R : Type u_1} {E₁ : Type u_2} {E₂ : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid E₁]
  [inst_2 : PartialOrder E₁] [inst_3 : AddCommMonoid E₂] [inst_4 : PartialOrder E₂] [inst_5 : Module R E₁]
  [inst_6 : Module R E₂] {S : Type u_5} [inst_7 : SMul S E₁] [inst_8 : SMul S E₂] [LinearMap.CompatibleSMul E₁ E₂ S R]
  (f : E₁ →ₚ[R] E₂) (c : S) (x : E₁), f (c • x) = c • f x

Defined in

Mathlib.Algebra.Order.Module.PositiveLinearMap

Cited by

1 results in Mathlib

Foundations

Depth 24 from the axioms · uses no axioms

Assumes

SemiringAddCommMonoidPartialOrderAddCommMonoidPartialOrderModuleModuleSMulSMulLinearMap.CompatibleSMul