Theorems · Theorem · group theory
Ring.mul_inverse_cancel
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] (x : M₀), IsUnit x → x * Ring.inverse x = 1- Cited by
- 6 results in Mathlib
- Foundations
- Depth 15 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- MonoidWithZerostatement and proof · cited by 456
- Ring.inversestatement · cited by 160
- Units.mul_invproof · cited by 67
- Ring.inverse_unitproof · cited by 24
Cited by6
Results whose statement or proof uses this declaration.
- MulChar.inv_applyproof · cited by 2
- hasSum_coe_mul_geometric_of_norm_lt_one'proof · cited by 2
- Polynomial.aeval_pow_two_pow_dvd_aeval_iterate_newtonMapproof · cited by 1
- Ring.mul_inverse_cancel_leftproof · cited by 1
- Ring.mul_inverse_cancel_rightproof · cited by 1
- Ring.isUnit_iff_mul_inverse_cancelproof · cited by 0