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feat(Algebra/Group): prod and pi instances for IsDedekindFinite #42927

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feat(Algebra/Group): prod and pi instances for IsDedekindFinite #42927

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5 changes: 5 additions & 0 deletions Mathlib/Algebra/Group/Pi/Basic.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -64,6 +64,11 @@ instance mulOneClass [∀ i, MulOneClass (f i)] : MulOneClass (∀ i, f i) where
one_mul := by intros; ext; exact one_mul _
mul_one := by intros; ext; exact mul_one _

@[to_additive]
instance [∀ i, MulOneClass (f i)] [∀ i, IsDedekindFiniteMonoid (f i)] :
IsDedekindFiniteMonoid (∀ i, f i) where
mul_eq_one_symm := by simp [funext_iff, mul_eq_one_comm]

@[to_additive]
instance invOneClass [∀ i, InvOneClass (f i)] : InvOneClass (∀ i, f i) where
inv_one := by ext; exact inv_one
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5 changes: 5 additions & 0 deletions Mathlib/Algebra/Group/Prod.lean
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Expand Up @@ -85,6 +85,11 @@ instance instMulOneClass [MulOneClass M] [MulOneClass N] : MulOneClass (M × N)
one_mul _ := by ext <;> exact one_mul _
mul_one _ := by ext <;> exact mul_one _

@[to_additive]
instance [MulOneClass M] [MulOneClass N] [IsDedekindFiniteMonoid M] [IsDedekindFiniteMonoid N] :
IsDedekindFiniteMonoid (M × N) where
mul_eq_one_symm := by simp [mul_eq_one_comm]

@[to_additive]
instance instMonoid [Monoid M] [Monoid N] : Monoid (M × N) :=
{ npow := fun z a => ⟨NPow.npow z a.1, NPow.npow z a.2⟩,
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