Theorems · Definition · ring theory
unitOfInvertible
{α : Type u} → [inst : Monoid α] → (a : α) → [Invertible a] → αˣAn Invertible element is a unit.
- Defined in
- Mathlib.Algebra.Group.Invertible.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
- Assumes
- MonoidInvertible
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.
- Monoidstatement and proof · cited by 3,887
- Unitsstatement · cited by 2,804
- Invertiblestatement and proof · cited by 549
- Invertible.invOfproof · cited by 268
Cited by11
Results whose statement or proof uses this declaration.
- isUnit_of_invertibleproof · cited by 26
- Ring.inverse_invertibleproof · cited by 11
- invOf_smul_smulproof · cited by 5
- Matrix.toLinearEquiv'proof · cited by 4
- Matrix.nonsingInvUnitproof · cited by 2
- PowerSeries.firstUnitCoeffproof · cited by 2
- smul_eq_iff_eq_invOf_smulproof · cited by 1
- Matrix.unitOfDetInvertibleproof · cited by 1
- smul_invOf_smulproof · cited by 0
- val_inv_unitOfInvertiblestatement and proof · cited by 0
- val_unitOfInvertiblestatement and proof · cited by 0