Theorems · Theorem · ring theory
OreLocalization.inv_def
∀ {R : Type u_1} [inst : MonoidWithZero R] [inst_1 : Nontrivial R] [inst_2 : OreLocalization.OreSet (nonZeroDivisors R)]
[inst_3 : NoZeroDivisors R] {r : R} {s : ↥(nonZeroDivisors R)}, (r /ₒ s)⁻¹ = if hr : r = 0 then 0 else ↑s /ₒ ⟨r, ⋯⟩- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement · cited by 3,086
- Nontrivialstatement and proof · cited by 2,416
- nonZeroDivisorsstatement and proof · cited by 895
- NoZeroDivisorsstatement and proof · cited by 545
- MonoidWithZerostatement and proof · cited by 456
- OreLocalization.OreSetstatement and proof · cited by 92
- OreLocalizationstatement · cited by 90
- OreLocalization.oreDivstatement and proof · cited by 72
- mem_nonZeroDivisors_of_ne_zerostatement · cited by 34
Cited by2
Results whose statement or proof uses this declaration.
- OreLocalization.mul_inv_cancelproof · cited by 0
- OreLocalization.inv_zeroproof · cited by 0