Theorems · Theorem · ring theory
IsUnit.nonempty_invertible
∀ {α : Type u} [inst : Monoid α] {a : α}, IsUnit a → Nonempty (Invertible a)- Defined in
- Mathlib.Algebra.Group.Invertible.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- Invertiblestatement and proof · cited by 549
- Invertible.copyproof · cited by 2
Cited by17
Results whose statement or proof uses this declaration.
- Matrix.nonsing_inv_mulproof · cited by 12
- Matrix.mul_nonsing_invproof · cited by 11
- IsUnit.invertibleproof · cited by 8
- Matrix.nonsing_inv_eq_ringInverseproof · cited by 7
- Matrix.det_nonsing_invproof · cited by 4
- CliffordAlgebra.isUnit_of_isUnit_ιproof · cited by 1
- CliffordAlgebra.isUnit_ι_of_isUnitproof · cited by 1
- Ring.inverse_add_inverseproof · cited by 1
- Ring.inverse_sub_inverseproof · cited by 1
- Matrix.inv_submatrix_equivproof · cited by 1
- IsUnit.algebraMap_of_algebraMapproof · cited by 0
- nonempty_invertible_iff_isUnitproof · cited by 0