Theorems · Theorem · group theory
Ring.inverse_mul_cancel
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] (x : M₀), IsUnit x → Ring.inverse x * 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.inv_mulproof · cited by 46
- Ring.inverse_unitproof · cited by 24
Cited by6
Results whose statement or proof uses this declaration.
- Ring.inverse_mul_cancel_leftproof · cited by 2
- Ring.inverse_mul_cancel_rightproof · cited by 1
- LinearMap.equivariantProjection_conditionproof · cited by 1
- Polynomial.roots_comp_C_mul_X_add_Cproof · cited by 0
- MulChar.inv_mulproof · cited by 0
- Ring.isUnit_iff_inverse_mul_cancelproof · cited by 0