Theorems · Theorem · functional analysis

SeminormFamily.comp_apply

∀ {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 : SeminormFamily 𝕜₂ F ι) (i : ι)
  (f : E →ₛₗ[σ₁₂] F), q.comp f i = (q i).comp f

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