Theorems · Theorem · group theory
mul_eq_zero_of_left
∀ {M₀ : Type u_1} [inst : MulZeroClass M₀] {a : M₀}, a = 0 → ∀ (b : M₀), a * b = 0- Defined in
- Mathlib.Algebra.GroupWithZero.Defs
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 5 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.
- MulZeroClass.zero_mulproof · cited by 1,625
- MulZeroClassstatement and proof · cited by 232
Cited by13
Results whose statement or proof uses this declaration.
- mul_eq_zeroproof · cited by 94
- left_ne_zero_of_mulproof · cited by 27
- tendsto_mul_nhds_zero_prod_of_disjoint_cocompactproof · cited by 2
- MvPolynomial.eval₂_C_mk_eq_zeroproof · cited by 2
- Units.mul_left_eq_zeroproof · cited by 2
- odd_sq_dvd_geom_sum₂_subproof · cited by 1
- Polynomial.X_pow_sub_X_sub_one_irreducibleproof · cited by 1
- Polynomial.eval₂_mul_eq_zero_of_leftproof · cited by 1
- Polynomial.Chebyshev.sumZeroes_T_of_not_dvdproof · cited by 1
- dvd_sub_pow_of_dvd_subproof · cited by 1
- Ideal.eval₂_C_mk_eq_zeroproof · cited by 0
- AddDissociated.randomisationproof · cited by 0