Theorems · Theorem · ring theory
mul_cancel_right_mem_nonZeroDivisors
∀ {R : Type u_1} [inst : Ring R] {x y r : R}, r ∈ nonZeroDivisors R → (x * r = y * r ↔ x = y)- Defined in
- Mathlib.Algebra.Ring.NonZeroDivisors
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Submonoidstatement · cited by 3,086
- nonZeroDivisorsstatement and proof · cited by 895
- mul_cancel_right_mem_nonZeroDivisorsRightproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- MvPowerSeries.invOfUnit_mulproof · cited by 2
- WeierstrassCurve.Jacobian.equiv_iff_eq_of_Z_eq'proof · cited by 1
- WeierstrassCurve.Projective.equiv_iff_eq_of_Z_eq'proof · cited by 1
- mul_cancel_right_coe_nonZeroDivisorsproof · cited by 0