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chore: make RingHom.id implicit-reducible #38509

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chore: make RingHom.id implicit-reducible #38509

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sgouezel Apr 25, 2026
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sgouezel Apr 25, 2026
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5 changes: 1 addition & 4 deletions Mathlib/Algebra/Algebra/Defs.lean
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Expand Up @@ -382,11 +382,8 @@ theorem coe_linearMap : ⇑(Algebra.linearMap R A) = algebraMap R A :=

/-- The identity map inducing an `Algebra` structure. -/
instance (priority := 1100) id : Algebra R R where
-- We override `toFun` and `toSMul` because `RingHom.id` is not reducible and cannot
-- be made so without a significant performance hit.
-- see library note [reducible non-instances].
toSMul := instSMulOfMul
__ := ({ RingHom.id R with toFun x := x }).toAlgebra
__ := (RingHom.id R).toAlgebra

@[simp] lemma linearMap_self : Algebra.linearMap R R = .id := rfl

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1 change: 1 addition & 0 deletions Mathlib/Algebra/Ring/Hom/Defs.lean
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Expand Up @@ -506,6 +506,7 @@ def mk' [NonAssocSemiring α] [NonAssocRing β] (f : α →* β)
variable {_ : NonAssocSemiring α} {_ : NonAssocSemiring β}

/-- The identity ring homomorphism from a semiring to itself. -/
@[implicit_reducible]
def id (α : Type*) [NonAssocSemiring α] : α →+* α where
toFun := _root_.id
map_zero' := rfl
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