Theorems · Theorem · ring theory
OreLocalization.mul_inv_cancel
∀ {R : Type u_1} [inst : MonoidWithZero R] [inst_1 : Nontrivial R] [inst_2 : OreLocalization.OreSet (nonZeroDivisors R)]
[inst_3 : NoZeroDivisors R] (x : OreLocalization (nonZeroDivisors R) R), x ≠ 0 → x * x⁻¹ = 1- Cited by
- 0 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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 and proof · cited by 90
- OreLocalization.oreDivproof · cited by 72
- mem_nonZeroDivisors_of_ne_zeroproof · cited by 34
- OreLocalization.indproof · cited by 18
- OreLocalization.one_defproof · cited by 10
- OreLocalization.zero_oreDiv'proof · cited by 3
- OreLocalization.inv_defproof · cited by 2
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