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set_option!
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adomani committed Apr 4, 2024
1 parent 3ac870b commit b348428
Showing 1 changed file with 3 additions and 1 deletion.
4 changes: 3 additions & 1 deletion Mathlib/RingTheory/Jacobson.lean
Original file line number Diff line number Diff line change
Expand Up @@ -474,6 +474,7 @@ section
variable {R : Type*} [CommRing R] [IsJacobson R]
variable (P : Ideal R[X]) [hP : P.IsMaximal]

set_option linter.terminalRefine false in
theorem isMaximal_comap_C_of_isMaximal [Nontrivial R] (hP' : ∀ x : R, C x ∈ P → x = 0) :
IsMaximal (comap (C : R →+* R[X]) P : Ideal R) := by
let P' := comap (C : R →+* R[X]) P
Expand All @@ -496,7 +497,8 @@ theorem isMaximal_comap_C_of_isMaximal [Nontrivial R] (hP' : ∀ x : R, C x ∈
suffices (⊥ : Ideal (Localization M)).IsMaximal by
rw [← IsLocalization.comap_map_of_isPrime_disjoint M (Localization M) ⊥ bot_prime
(disjoint_iff_inf_le.mpr fun x hx => hM (hx.2 ▸ hx.1))]
exact ((isMaximal_iff_isMaximal_disjoint (Localization M) _ _).mp (by rwa [map_bot])).1
-- a terminal `refine'` that cannot be replaced by either a `refine` nor an `exact!
refine' ((isMaximal_iff_isMaximal_disjoint (Localization M) _ _).mp (by rwa [map_bot])).1
let M' : Submonoid (R[X] ⧸ P) := M.map φ
have hM' : (0 : R[X] ⧸ P) ∉ M' := fun ⟨z, hz⟩ =>
hM (quotientMap_injective (_root_.trans hz.2 φ.map_zero.symm) ▸ hz.1)
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