Theorems · Theorem · group theory
left_ne_zero_of_mul
∀ {M₀ : Type u_1} [inst : MulZeroClass M₀] {a b : M₀}, a * b ≠ 0 → a ≠ 0- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- MulZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulZeroClassstatement and proof · cited by 232
- mul_eq_zero_of_leftproof · cited by 13
Cited by27
Results whose statement or proof uses this declaration.
- Prime.irreducibleproof · cited by 54
- ne_zero_of_dvd_ne_zeroproof · cited by 26
- left_ne_zero_of_mul_eq_oneproof · cited by 6
- Nat.totient_mulproof · cited by 5
- ne_zero_and_ne_zero_of_mulproof · cited by 3
- map_le_lineMap_iff_slope_le_slope_leftproof · cited by 3
- MvPowerSeries.coeff_monomial_mulproof · cited by 3
- ArithmeticFunction.coe_zeta_smul_applyproof · cited by 3
- Nat.multiplicative_factorizationproof · cited by 3
- Polynomial.rootMultiplicity_mulproof · cited by 3
- Nat.map_div_right_divisorsproof · cited by 3
- Polynomial.support_scaleRoots_leproof · cited by 3