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Merge pull request #84 from GTBarkley/grant

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added WF_interval_le_prime
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GTBarkley 2023-06-15 21:58:00 -07:00 committed by GitHub
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1 changed files with 14 additions and 3 deletions
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CommAlg/grant2.lean
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@ -54,9 +54,20 @@ def symbolicIdeal(Q : Ideal R) {hin : Q.IsPrime} (I : Ideal R) : Ideal R where
rw [←mul_assoc, mul_comm s, mul_assoc]
exact Ideal.mul_mem_left _ _ hs2
theorem WF_interval_le_prime (I : Ideal R) (P : Ideal R) [P.IsPrime]
(h : ∀ J ∈ (Set.Icc I P), J.IsPrime → J = P ):
WellFounded ((· < ·) : (Set.Icc I P) → (Set.Icc I P) → Prop ) := sorry
protected lemma LocalRing.height_le_one_of_minimal_over_principle
[LocalRing R] (q : PrimeSpectrum R) {x : R}
[LocalRing R] {x : R}
(h : (closedPoint R).asIdeal ∈ (Ideal.span {x}).minimalPrimes) :
q = closedPoint R ∨ Ideal.height q = 0 := by
Ideal.height (closedPoint R) ≤ 1 := by
-- by_contra hcont
-- push_neg at hcont
-- rw [Ideal.lt_height_iff'] at hcont
-- rcases hcont with ⟨c, hc1, hc2, hc3⟩
apply height_le_of_gt_height_lt
intro p hp
sorry