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Mathlib.Algebra.GroupWithZero.Action.TransferInstance

Transfer algebraic structures across Equivs #

This continues the pattern set in Mathlib/Algebra/Group/TransferInstance.lean.

@[reducible, inline]
abbrev Equiv.smulZeroClass (M : Type u_1) {A : Type u_3} {B : Type u_4} (e : A ≃ B) [Zero B] [SMulZeroClass M B] :

Transfer SMulZeroClass across an Equiv

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      @[reducible, inline]
      abbrev Equiv.smulWithZero (M₀ : Type u_2) {A : Type u_3} {B : Type u_4} (e : A ≃ B) [Zero M₀] [Zero B] [SMulWithZero M₀ B] :
      SMulWithZero Mâ‚€ A

      Transfer SMulWithZero across an Equiv

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          @[reducible, inline]
          abbrev Equiv.mulActionWithZero (M₀ : Type u_2) {A : Type u_3} {B : Type u_4} (e : A ≃ B) [MonoidWithZero M₀] [Zero B] [MulActionWithZero M₀ B] :
          MulActionWithZero Mâ‚€ A

          Transfer MulActionWithZero across an Equiv

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              @[reducible, inline]
              abbrev Equiv.distribSMul (M : Type u_1) {A : Type u_3} {B : Type u_4} (e : A ≃ B) [AddZeroClass B] [DistribSMul M B] :

              Transfer DistribSMul across an Equiv

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                  @[reducible, inline]
                  abbrev Equiv.distribMulAction (M : Type u_1) {A : Type u_3} {B : Type u_4} (e : A ≃ B) [Monoid M] [AddMonoid B] [DistribMulAction M B] :

                  Transfer DistribMulAction across an Equiv

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                    Instances For