Theorems · Theorem · commutative algebra
FractionalIdeal.mul_inv_cancel_of_le_one
∀ {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 ≤ 1 → ↑I * (↑I)⁻¹ = 1- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Algebrastatement and proof · cited by 11,388
- Top.topproof · 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
- nonZeroDivisorsstatement and proof · cited by 895
- IsFractionRingstatement and proof · cited by 738
- IsDedekindDomainstatement and proof · cited by 668
- FractionalIdealstatement and proof · cited by 423
- eq_bot_iffproof · cited by 159
- FractionalIdeal.coeIdealstatement and proof · cited by 109
Cited by1
Results whose statement or proof uses this declaration.
- FractionalIdeal.coe_ideal_mul_invproof · cited by 1