Theorems · Theorem · commutative algebra
Ideal.height_lt_top_of_isPrime
∀ {R : Type u_1} [inst : CommRing R] {I : Ideal R} [I.FiniteHeight] [I.IsPrime], I.height < ⊤- Defined in
- Mathlib.RingTheory.Ideal.Height
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Top.topstatement · cited by 9,680
- ENatstatement · cited by 4,985
- Idealstatement and proof · cited by 4,748
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.heightstatement · cited by 83
- Ideal.IsPrime.ne_topproof · cited by 82
- Ideal.FiniteHeightstatement and proof · cited by 18
- Ideal.height_lt_topproof · cited by 4
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