Documentation

Mathlib.Algebra.Order.GroupWithZero.Action.Synonym

Actions by and on order synonyms #

This PR transfers group action with zero instances from a type α to αᵒᵈ and Lex α. Note that the SMul instances are already defined in Mathlib.Algebra.Order.Group.Synonym.

See also #

source
instance OrderDual.instSMulWithZero {G₀ : Type u_1} {M₀ : Type u_2} [Zero G₀] [Zero M₀] [SMulWithZero G₀ M₀] :
SMulWithZero G₀ᵒᵈ M₀
Equations
  • OrderDual.instSMulWithZero = inst✝
source
instance OrderDual.instSMulWithZero' {G₀ : Type u_1} {M₀ : Type u_2} [Zero G₀] [Zero M₀] [SMulWithZero G₀ M₀] :
SMulWithZero G₀ M₀ᵒᵈ
Equations
  • OrderDual.instSMulWithZero' = inst✝
source
instance OrderDual.instDistribSMul {G₀ : Type u_1} {M₀ : Type u_2} [AddZeroClass M₀] [DistribSMul G₀ M₀] :
DistribSMul G₀ᵒᵈ M₀
Equations
  • OrderDual.instDistribSMul = inst✝
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instance OrderDual.instDistribSMul' {G₀ : Type u_1} {M₀ : Type u_2} [AddZeroClass M₀] [DistribSMul G₀ M₀] :
DistribSMul G₀ M₀ᵒᵈ
Equations
  • OrderDual.instDistribSMul' = inst✝
source
instance OrderDual.instDistribMulAction {G₀ : Type u_1} {M₀ : Type u_2} [Monoid G₀] [AddMonoid M₀] [DistribMulAction G₀ M₀] :
DistribMulAction G₀ᵒᵈ M₀
Equations
  • OrderDual.instDistribMulAction = inst✝
source
instance OrderDual.instDistribMulAction' {G₀ : Type u_1} {M₀ : Type u_2} [Monoid G₀] [AddMonoid M₀] [DistribMulAction G₀ M₀] :
DistribMulAction G₀ M₀ᵒᵈ
Equations
  • OrderDual.instDistribMulAction' = inst✝
source
instance OrderDual.instMulActionWithZero {G₀ : Type u_1} {M₀ : Type u_2} [MonoidWithZero G₀] [AddMonoid M₀] [MulActionWithZero G₀ M₀] :
MulActionWithZero G₀ᵒᵈ M₀
Equations
  • OrderDual.instMulActionWithZero = inst✝
source
instance OrderDual.instMulActionWithZero' {G₀ : Type u_1} {M₀ : Type u_2} [MonoidWithZero G₀] [AddMonoid M₀] [MulActionWithZero G₀ M₀] :
MulActionWithZero G₀ M₀ᵒᵈ
Equations
  • OrderDual.instMulActionWithZero' = inst✝
source
instance Lex.instSMulWithZero {G₀ : Type u_1} {M₀ : Type u_2} [Zero G₀] [Zero M₀] [SMulWithZero G₀ M₀] :
SMulWithZero (Lex G₀) M₀
Equations
  • Lex.instSMulWithZero = inst✝
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instance Lex.instSMulWithZero' {G₀ : Type u_1} {M₀ : Type u_2} [Zero G₀] [Zero M₀] [SMulWithZero G₀ M₀] :
SMulWithZero G₀ (Lex M₀)
Equations
  • Lex.instSMulWithZero' = inst✝
source
instance Lex.instDistribSMul {G₀ : Type u_1} {M₀ : Type u_2} [AddZeroClass M₀] [DistribSMul G₀ M₀] :
DistribSMul (Lex G₀) M₀
Equations
  • Lex.instDistribSMul = inst✝
source
instance Lex.instDistribSMul' {G₀ : Type u_1} {M₀ : Type u_2} [AddZeroClass M₀] [DistribSMul G₀ M₀] :
DistribSMul G₀ (Lex M₀)
Equations
  • Lex.instDistribSMul' = inst✝
source
instance Lex.instDistribMulAction {G₀ : Type u_1} {M₀ : Type u_2} [Monoid G₀] [AddMonoid M₀] [DistribMulAction G₀ M₀] :
DistribMulAction (Lex G₀) M₀
Equations
  • Lex.instDistribMulAction = inst✝
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instance Lex.instDistribMulAction' {G₀ : Type u_1} {M₀ : Type u_2} [Monoid G₀] [AddMonoid M₀] [DistribMulAction G₀ M₀] :
DistribMulAction G₀ (Lex M₀)
Equations
  • Lex.instDistribMulAction' = inst✝
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instance Lex.instMulActionWithZero {G₀ : Type u_1} {M₀ : Type u_2} [MonoidWithZero G₀] [AddMonoid M₀] [MulActionWithZero G₀ M₀] :
MulActionWithZero (Lex G₀) M₀
Equations
  • Lex.instMulActionWithZero = inst✝
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instance Lex.instMulActionWithZero' {G₀ : Type u_1} {M₀ : Type u_2} [MonoidWithZero G₀] [AddMonoid M₀] [MulActionWithZero G₀ M₀] :
MulActionWithZero G₀ (Lex M₀)
Equations
  • Lex.instMulActionWithZero' = inst✝