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Theorems · Definition · functional analysis

NormedSpace.ofCore

{𝕜 : Type u_8} →
  {E : Type u_9} →
    [inst : NormedField 𝕜] →
      [inst_1 : SeminormedAddCommGroup E] → [inst_2 : Module 𝕜 E] → NormedSpace.Core 𝕜 E → NormedSpace 𝕜 E

Produces a NormedSpace 𝕜 E instance from a NormedSpace.Core. This is meant to be used on types where the NormedAddCommGroup E instance has also been defined using core. See note [reducible non-instances].

Defined in
Mathlib.Analysis.Normed.Module.Basic
Cited by
1 results in Mathlib
Foundations
Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedFieldSeminormedAddCommGroupModule
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CStarModule.norm_eq_csSup · cited by 0CStarModule.norm_eq_csSupModule · cited by 20661ModuleNormedSpace · cited by 12499NormedSpaceSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupNormedField · cited by 1084NormedFieldNormedSpace.Core · cited by 5NormedSpace.CoreNormedSpace.ofCoreCITED BYCITES

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