Theorems · Theorem · group theory
Ring.inverse_mul_eq_iff_eq_mul
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] (x y z : M₀), IsUnit x → (Ring.inverse x * y = z ↔ y = x * z)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 17 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsUnitstatement and proof · cited by 1,602
- MonoidWithZerostatement and proof · cited by 456
- Ring.inversestatement and proof · cited by 160
- Ring.inverse_mul_cancel_leftproof · cited by 2
- Ring.mul_inverse_cancel_leftproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- DividedPowers.OfInvertibleFactorial.dpow_comp_of_mul_ltproof · cited by 1
- Ring.inverse_pow_mul_eq_iff_eq_mulproof · cited by 1
- DividedPowers.OfInvertibleFactorial.dpow_mul_of_add_ltproof · cited by 1
- DividedPowers.OfInvertibleFactorial.dpow_add_of_ltproof · cited by 1
- DividedPowers.RatAlgebra.dividedPowers_uniqueproof · cited by 0
- Polynomial.isFixedPt_newtonMap_of_isUnit_iffproof · cited by 0