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Turn some simp into simp only

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This commit is contained in:
Sayantan Santra 2023-06-14 11:12:33 -07:00
parent 50515d9ed8
commit a2f481c7db
Signed by: SinTan1729
GPG key ID: EB3E68BFBA25C85F
2 changed files with 9 additions and 4 deletions
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2
CommAlg/krull.lean
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@ -63,7 +63,7 @@ lemma krullDim_eq_height [LocalRing R] : krullDim R = height (closedPoint R) :=
apply height_le_of_le
apply le_maximalIdeal
exact I.2.1
. simp
. simp only [height_le_krullDim]
#check height_le_krullDim
--some propositions that would be nice to be able to eventually

9
CommAlg/sayantan(dim_eq_dim_polynomial_add_one).lean
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@ -42,16 +42,21 @@ lemma dim_eq_dim_polynomial_add_one [Nontrivial R] [IsNoetherianRing R] :
have PleP' : P ≤ P' := PleM
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
sorry
obtain ⟨I, h⟩ := this
use I
exact ge_trans h this
obtain ⟨I, IP⟩ := this
have : (↑(height I + 1) : WithBot ℕ∞) ≤ ⨆ (I : PrimeSpectrum R), ↑(height I + 1) := by
apply @le_iSup (WithBot ℕ∞) _ _ _ I
apply ge_trans this IP
exact ge_trans this IP
have oneOut : (⨆ (I : PrimeSpectrum R), (height I : WithBot ℕ∞) + 1) ≤ (⨆ (I : PrimeSpectrum R), ↑(height I)) + 1 := by
have : ∀ P : PrimeSpectrum R, (height P : WithBot ℕ∞) + 1 ≤ (⨆ (I : PrimeSpectrum R), ↑(height I)) + 1 :=
fun P ↦ (by apply add_le_add_right (@le_iSup (WithBot ℕ∞) _ _ _ P) 1)
apply iSup_le
apply this
simp
simp only [iSup_le_iff]
intro P
exact ge_trans oneOut (htPBdd P)