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Trying to break it down to smaller parts

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Sayantan Santra 2023-06-14 17:01:34 -07:00
parent c64025b1b4
commit 70007679cd
Signed by: SinTan1729
GPG key ID: EB3E68BFBA25C85F
1 changed files with 10 additions and 0 deletions
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CommAlg/sayantan(dim_eq_dim_polynomial_add_one).lean
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@ -3,9 +3,11 @@ import Mathlib.Order.Height
import Mathlib.RingTheory.PrincipalIdealDomain
import Mathlib.RingTheory.DedekindDomain.Basic
import Mathlib.RingTheory.Ideal.Quotient
import Mathlib.RingTheory.Ideal.MinimalPrime
import Mathlib.RingTheory.Localization.AtPrime
import Mathlib.AlgebraicGeometry.PrimeSpectrum.Basic
import Mathlib.Order.ConditionallyCompleteLattice.Basic
import Mathlib.Data.Set.Ncard
namespace Ideal
@ -24,6 +26,13 @@ lemma dim_le_dim_polynomial_add_one [Nontrivial R] :
lemma height_le_of_le {I J : PrimeSpectrum R} (I_le_J : I ≤ J) : height I ≤ height J := sorry -- Already done in main file
lemma primeIdeal_finite_height_of_noetherianRing [Nontrivial R] [IsNoetherianRing R] (P: PrimeSpectrum R) : height P ≠ ⊤ := by
sorry
lemma exist_elts_MinimalOver_of_primeIdeal_of_noetherianRing [Nontrivial R] [IsNoetherianRing R] (P: PrimeSpectrum R) :
∃S : Set R, Set.ncard s = height P ∧ P.asIdeal ∈ Ideal.minimalPrimes (Ideal.span S) := by
sorry
lemma dim_eq_dim_polynomial_add_one [Nontrivial R] [IsNoetherianRing R] :
krullDim R + 1 = krullDim (Polynomial R) := by
rw [le_antisymm_iff]
@ -43,6 +52,7 @@ lemma dim_eq_dim_polynomial_add_one [Nontrivial R] [IsNoetherianRing R] :
have : height P ≤ height P' := height_le_of_le PleP'
simp only [WithBot.coe_le_coe]
have : ∃ (I : PrimeSpectrum R), height P' ≤ height I + 1 := by
-- Prime avoidance is called subset_union_prime
sorry
obtain ⟨I, h⟩ := this