Theorems · Theorem · ring theory
isUnit_of_invertible
∀ {α : Type u} [inst : Monoid α] (a : α) [Invertible a], IsUnit a- Defined in
- Mathlib.Algebra.Group.Invertible.Basic
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 8 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
- IsUnitstatement · cited by 1,602
- Invertiblestatement and proof · cited by 549
- unitOfInvertibleproof · cited by 7
Cited by26
Results whose statement or proof uses this declaration.
- Matrix.isUnit_det_of_invertibleproof · cited by 6
- AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.mk_mem_carrierproof · cited by 5
- Matrix.isUnit_det_of_left_inverseproof · cited by 5
- QuadraticMap.radical_eq_ker_polarBilinproof · cited by 3
- CharP.isUnit_natCast_iffproof · cited by 3
- AffineEquiv.injective_pointReflection_left_of_moduleproof · cited by 2
- NormedSpace.isUnit_exp_of_mem_ballproof · cited by 1
- AlgebraicGeometry.injective_germ_basicOpenproof · cited by 1
- CliffordAlgebra.isUnit_of_isUnit_ιproof · cited by 1
- Matrix.isUnit_det_of_right_inverseproof · cited by 1
- CliffordAlgebra.isUnit_ι_of_isUnitproof · cited by 1
- Polynomial.rootMultiplicity_comp_C_mul_X_add_Cproof · cited by 1