Theorems · Theorem · ring theory
invOf_units
∀ {α : Type u} [inst : Monoid α] (u : αˣ) [inst_1 : Invertible ↑u], ⅟↑u = ↑u⁻¹- Defined in
- Mathlib.Algebra.Group.Invertible.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- MonoidInvertible
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- Invertiblestatement and proof · cited by 549
- Invertible.invOfstatement · cited by 268
- Units.mul_invproof · cited by 67
- invOf_eq_right_invproof · cited by 10
Cited by7
Results whose statement or proof uses this declaration.
- Matrix.coe_units_invproof · cited by 14
- hasFDerivAt_ringInverseproof · cited by 5
- CFC.inverse_eq_rpow_neg_oneproof · cited by 4
- lipschitzGroup.conjAct_smul_ι_mem_range_ιproof · cited by 3
- lipschitzGroup.involute_act_ι_mem_range_ιproof · cited by 2
- ContinuousLinearMap.ringInverse_equivproof · cited by 1
- Matrix.GeneralLinearGroup.det_surjectiveproof · cited by 1