Theorems · Theorem · group theory
Ring.isUnit_iff_mul_inverse_cancel
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] {x : M₀}, IsUnit x ↔ x * Ring.inverse x = 1- Cited by
- 0 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nontrivialproof · cited by 2,416
- MulZeroClass.mul_zeroproof · cited by 2,091
- IsUnitstatement · cited by 1,602
- MonoidWithZerostatement and proof · cited by 456
- Ring.inversestatement and proof · cited by 160
- Ring.inverse_non_unitproof · cited by 26
- Ring.mul_inverse_cancelproof · cited by 6
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