Theorems · Theorem · functional analysis

Seminorm.add_comp

∀ {𝕜 : Type u_3} {𝕜₂ : Type u_4} {E : Type u_7} {E₂ : Type u_8} [inst : SeminormedRing 𝕜] [inst_1 : SeminormedRing 𝕜₂]
  {σ₁₂ : 𝕜 →+* 𝕜₂} [inst_2 : RingHomIsometric σ₁₂] [inst_3 : AddCommGroup E] [inst_4 : AddCommGroup E₂]
  [inst_5 : Module 𝕜 E] [inst_6 : Module 𝕜₂ E₂] (p q : Seminorm 𝕜₂ E₂) (f : E →ₛₗ[σ₁₂] E₂),
  (p + q).comp f = p.comp f + q.comp f

Defined in

Mathlib.Analysis.Seminorm

Cited by

0 results in Mathlib

Foundations

Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedRingSeminormedRingRingHomIsometricAddCommGroupAddCommGroupModuleModule