Theorems · Theorem · functional analysis

SeminormFamily.comp.congr_simp

∀ {𝕜 : Type u_2} {𝕜₂ : Type u_3} {E : Type u_6} {F : Type u_7} {ι : Type u_9} [inst : NormedField 𝕜]
  [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E] [inst_3 : NormedField 𝕜₂] [inst_4 : AddCommGroup F]
  [inst_5 : Module 𝕜₂ F] {σ₁₂ : 𝕜 →+* 𝕜₂} [inst_6 : RingHomIsometric σ₁₂] (q q_1 : SeminormFamily 𝕜₂ F ι),
  q = q_1 → ∀ (f f_1 : E →ₛₗ[σ₁₂] F), f = f_1 → ∀ (a a_1 : ι), a = a_1 → q.comp f a = q_1.comp f_1 a_1

Defined in

Mathlib.Analysis.LocallyConvex.WithSeminorms

Cited by

0 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupModuleNormedFieldAddCommGroupModuleRingHomIsometric