Theorems · Theorem · group theory
CommGroupWithZero.mul_inv_cancel
∀ {G₀ : Type u_2} [self : CommGroupWithZero G₀] (a : G₀), a ≠ 0 → a * a⁻¹ = 1Every nonzero element of a group with zero is invertible.
- Defined in
- Mathlib.Algebra.GroupWithZero.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- CommGroupWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommGroupWithZerostatement and proof · cited by 94
- Monoid.toOnestatement · cited by 34
- CommMonoidWithZero.toZerostatement · cited by 10
- CommGroupWithZero.toInvstatement · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.memLp_enorm_rpow_iffproof · cited by 1
- Function.Injective.semifieldproof · cited by 0