Theorems · Theorem · group theory
Ring.inverse_unit
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] (u : M₀ˣ), Ring.inverse ↑u = ↑u⁻¹By definition, if x is invertible then inverse x = x⁻¹.
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidWithZero
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.
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- MonoidWithZerostatement and proof · cited by 456
- Ring.inversestatement · cited by 160
- Units.isUnitproof · cited by 116
- IsUnit.unit_of_val_unitsproof · cited by 5
Cited by24
Results whose statement or proof uses this declaration.
- Ring.inverse_invertibleproof · cited by 11
- Ring.mul_inverse_cancelproof · cited by 6
- Ring.inverse_mul_cancelproof · cited by 6
- cfc_inv_idproof · cited by 5
- Ring.inverse_oneproof · cited by 5
- NormedRing.inverse_one_subproof · cited by 4
- Ring.inverse_eq_invproof · cited by 4
- NormedRing.inverse_continuousAtproof · cited by 3
- cfc_invproof · cited by 3
- spectrum.hasDerivAt_resolvent_const_leftproof · cited by 3
- analyticAt_inverseproof · cited by 3
- NormedRing.inverse_addproof · cited by 2