Theorems · Theorem · field theory
DivisionSemiring.mul_inv_cancel
∀ {K : Type u_2} [self : DivisionSemiring K] (a : K), a ≠ 0 → a * a⁻¹ = 1Every nonzero element of a group with zero is invertible.
- Defined in
- Mathlib.Algebra.Field.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- DivisionSemiring
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Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoid.toZerostatement · cited by 325
- DivisionSemiringstatement and proof · cited by 216
- Monoid.toOnestatement · cited by 34
- DivisionSemiring.toInvstatement · cited by 4
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