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[Merged by Bors] - chore(RingTheory/Smooth/Basic): fix namespace of mvPolynomial instance #39706

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[Merged by Bors] - chore(RingTheory/Smooth/Basic): fix namespace of mvPolynomial instance #39706

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c64e500
fix namespace issue
justus-springer May 22, 2026
a6adcfe
Apply suggestion from @ocfnash
justus-springer May 25, 2026
5da6d34
update deprecation
justus-springer May 25, 2026
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4 changes: 3 additions & 1 deletion Mathlib/RingTheory/Smooth/Basic.lean
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Expand Up @@ -108,7 +108,7 @@ lemma FormallySmooth.comp_surjective [FormallySmooth R A] (I : Ideal B) (hI : I
exact ⟨l.comp g, by rw [← AlgHom.comp_assoc, ← this, AlgHom.comp_assoc, hg, AlgHom.comp_id]⟩

set_option backward.isDefEq.respectTransparency false in
instance mvPolynomial (σ : Type*) : FormallySmooth R (MvPolynomial σ R) := by
instance instFormallySmoothMvPolynomial (σ : Type*) : FormallySmooth R (MvPolynomial σ R) := by
let P : Generators R (MvPolynomial σ R) σ :=
.ofSurjective X (by simp [aeval_X_left, Function.Surjective])
have : Subsingleton ↥P.toExtension.ker :=
Expand All @@ -118,6 +118,8 @@ instance mvPolynomial (σ : Type*) : FormallySmooth R (MvPolynomial σ R) := by
have := P.toExtension.h1Cotangentι_injective.subsingleton
exact ⟨inferInstance, P.equivH1Cotangent.symm.subsingleton⟩

@[deprecated (since := "2026-05-22")] alias mvPolynomial := instFormallySmoothMvPolynomial

end

namespace FormallySmooth
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4 changes: 2 additions & 2 deletions Mathlib/RingTheory/Smooth/Quotient.lean
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Expand Up @@ -104,14 +104,14 @@ lemma Algebra.FormallySmooth.of_surjective_of_ker_eq_map_of_flat [Module.Flat R
(sq0 : (RingHom.ker (algebraMap R R')) ^ 2 = ⊥) (smoothq : Algebra.FormallySmooth R' S') :
Algebra.FormallySmooth R S := by
let P := (Algebra.Generators.self R S).toExtension
let : Algebra.FormallySmooth R P.Ring := Algebra.mvPolynomial S
let : Algebra.FormallySmooth R P.Ring := instFormallySmoothMvPolynomial S
let IP := (RingHom.ker (algebraMap R R')).map (algebraMap R P.Ring)
let Gen : Algebra.Generators R' S' S := {
val := algebraMap S S'
σ' := fun s' ↦ MvPolynomial.X (Classical.choose (surjS s'))
aeval_val_σ' s' := by simp [Classical.choose_spec (surjS s')] }
let P' := Gen.toExtension
let : Algebra.FormallySmooth R' P'.Ring := Algebra.mvPolynomial S
let : Algebra.FormallySmooth R' P'.Ring := instFormallySmoothMvPolynomial S
let : Algebra P.Ring P'.Ring := MvPolynomial.algebraMvPolynomial
let : IsScalarTower R P.Ring P'.Ring :=
IsScalarTower.of_algebraMap_eq (fun x ↦ (MvPolynomial.map_C _ x).symm)
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