Theorems · Theorem · commutative algebra
Ideal.height_add_one_le_of_lt_of_isPrime
∀ {R : Type u_1} [inst : CommRing R] {I J : Ideal R} [I.IsPrime] [J.IsPrime], I < J → I.height + 1 ≤ J.height- Defined in
- Mathlib.RingTheory.Ideal.Height
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- ENatstatement · cited by 4,985
- Idealstatement and proof · cited by 4,748
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.heightstatement · cited by 83
- Order.height_add_one_leproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.height_strict_mono_of_isPrimeproof · cited by 4
- IsPrincipalIdealRing.height_eq_one_of_isMaximalproof · cited by 0