diff --git a/CommAlg/krull.lean b/CommAlg/krull.lean index bd9edb4..1c70814 100644 --- a/CommAlg/krull.lean +++ b/CommAlg/krull.lean @@ -86,7 +86,7 @@ lemma le_krullDim_iff (R : Type _) [CommRing R] (n : ℕ) : fun _ ↦ (WithBot.coe_le rfl).mpr (H1 _) rw [←iSup_le_iff] at H1 have : ((n : ℕ∞) : WithBot ℕ∞) ≤ (((n - 1 : ℕ) : ℕ∞) : WithBot ℕ∞) := le_trans H H1 - norm_cast at this + norm_cast at this have that : n - 1 < n := by refine Nat.sub_lt h (by norm_num) apply lt_irrefl (n-1) (trans that this) · rintro ⟨I, h⟩ @@ -278,7 +278,7 @@ lemma domain_dim_zero.isField {D: Type _} [CommRing D] [IsDomain D] (h: krullDim have : {J | J < P'}.Nonempty := Set.nonempty_of_mem this unfold height rw [←Set.one_le_chainHeight_iff] at this - exact not_le_of_gt (Iff.mp ENat.one_le_iff_pos this) + exact not_le_of_gt (ENat.one_le_iff_pos.mp this) have nonpos_height : height P' ≤ 0 := by have := height_le_krullDim P' rw [h] at this