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[Merged by Bors] - fix(ring_theory/dedekind_domain): Speed up ideal.unique_factorization_monoid #9243

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[Merged by Bors] - fix(ring_theory/dedekind_domain): Speed up ideal.unique_factorization_monoid #9243

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27 changes: 14 additions & 13 deletions src/ring_theory/dedekind_domain.lean
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Expand Up @@ -664,19 +664,20 @@ instance : wf_dvd_monoid (ideal A) :=
instance ideal.unique_factorization_monoid :
unique_factorization_monoid (ideal A) :=
{ irreducible_iff_prime := λ P,
⟨λ hirr, ⟨hirr.ne_zero, hirr.not_unit, λ I J, begin
have : P.is_maximal,
{ use mt ideal.is_unit_iff.mpr hirr.not_unit,
intros J hJ,
obtain ⟨J_ne, H, hunit, P_eq⟩ := ideal.dvd_not_unit_iff_lt.mpr hJ,
exact ideal.is_unit_iff.mp ((hirr.is_unit_or_is_unit P_eq).resolve_right hunit) },
simp only [ideal.dvd_iff_le, has_le.le, preorder.le, partial_order.le],
contrapose!,
rintros ⟨⟨x, x_mem, x_not_mem⟩, ⟨y, y_mem, y_not_mem⟩⟩,
exact ⟨x * y, ideal.mul_mem_mul x_mem y_mem,
mt this.is_prime.mem_or_mem (not_or x_not_mem y_not_mem)⟩,
end⟩,
prime.irreducible⟩,
⟨λ hirr, ⟨hirr.ne_zero, hirr.not_unit, λ I J, begin
have : P.is_maximal,
{ refine ⟨⟨mt ideal.is_unit_iff.mpr hirr.not_unit, _⟩⟩,
intros J hJ,
obtain ⟨J_ne, H, hunit, P_eq⟩ := ideal.dvd_not_unit_iff_lt.mpr hJ,
exact ideal.is_unit_iff.mp ((hirr.is_unit_or_is_unit P_eq).resolve_right hunit) },
rw [ideal.dvd_iff_le, ideal.dvd_iff_le, ideal.dvd_iff_le,
set_like.le_def, set_like.le_def, set_like.le_def],
contrapose!,
rintros ⟨⟨x, x_mem, x_not_mem⟩, ⟨y, y_mem, y_not_mem⟩⟩,
exact ⟨x * y, ideal.mul_mem_mul x_mem y_mem,
mt this.is_prime.mem_or_mem (not_or x_not_mem y_not_mem)⟩,
end⟩,
prime.irreducible⟩,
.. ideal.wf_dvd_monoid }

noncomputable instance ideal.normalization_monoid : normalization_monoid (ideal A) :=
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