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Theorems · Theorem · number theory

LinearOrderedCommGroupWithZero.mul_inv_cancel

∀ {α : Type u_3} [self : LinearOrderedCommGroupWithZero α] (a : α), a ≠ 0 → a * a⁻¹ = 1

Every nonzero element of a group with zero is invertible.

Defined in
Mathlib.Algebra.Order.GroupWithZero.Canonical
Cited by
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Foundations
Depth 4 from the axioms · uses no axioms
Assumes
LinearOrderedCommGroupWithZero

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