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Mathlib.Analysis.Normed.Module.TransferInstance

Transfer normed algebraic structures across Equivs #

In this file, we transfer a (semi-)normed (additive) commutative group and normed space structures across an equivalence. This continues the pattern set in Mathlib/Algebra/Module/TransferInstance.lean.

@[reducible, inline]
abbrev Equiv.seminormedCommGroup {α : Type u_1} {β : Type u_2} [SeminormedCommGroup β] (e : α β) :

Transfer a SeminormedCommGroup across an Equiv

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      @[reducible, inline]

      Transfer a SeminormedAddCommGroup across an Equiv

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          @[reducible, inline]
          abbrev Equiv.normedCommGroup {α : Type u_1} {β : Type u_2} [NormedCommGroup β] (e : α β) :

          Transfer a NormedCommGroup across an Equiv

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              @[reducible, inline]
              abbrev Equiv.normedAddCommGroup {α : Type u_1} {β : Type u_2} [NormedAddCommGroup β] (e : α β) :

              Transfer a NormedAddCommGroup across an Equiv

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                  @[reducible, inline]
                  abbrev Equiv.normedSpace {α : Type u_1} {β : Type u_2} (𝕜 : Type u_3) [NormedField 𝕜] [SeminormedAddCommGroup β] [NormedSpace 𝕜 β] (e : α β) :
                  NormedSpace 𝕜 α

                  Transfer NormedSpace across an Equiv

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