Theorems · Theorem · commutative algebra
FractionalIdeal.not_inv_le_one_of_ne_bot
∀ {A : Type u_2} {K : Type u_3} [inst : CommRing A] [inst_1 : Field K] [inst_2 : Algebra A K]
[inst_3 : IsFractionRing A K] [inst_4 : IsDedekindDomain A] {I : Ideal A}, I ≠ ⊥ → I ≠ ⊤ → ¬(↑I)⁻¹ ≤ 1- Cited by
- 2 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites53
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Top.topstatement and proof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- Multisetproof · cited by 2,627
- mul_commproof · cited by 2,262
- mul_assocproof · cited by 1,667
Cited by2
Results whose statement or proof uses this declaration.
- FractionalIdeal.mul_inv_cancel_of_le_oneproof · cited by 1
- FractionalIdeal.exists_notMem_one_of_ne_botproof · cited by 0