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Theorems · Theorem · group theory

mul_eq_zero_iff_right

∀ {M₀ : Type u_1} [inst : MulZeroClass M₀] [NoZeroDivisors M₀] {a b : M₀}, b ≠ 0 → (a * b = 0 ↔ a = 0)
Defined in
Mathlib.Algebra.GroupWithZero.Defs
Cited by
5 results in Mathlib
Foundations
Depth 8 from the axioms · uses propext
Assumes
MulZeroClassNoZeroDivisors
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Polynomial.Chebyshev.roots_U_real · cited by 2Chebyshev.roots_U_realComplex.sq_nonneg_iff · cited by 1Complex.sq_nonneg_iffNumberField.Units.regOfFamily_div_regOfFamily · cited by 1Units.regOfFamily_div_reg…Similar.angle_eq · cited by 1Similar.angle_eqComplex.sq_nonpos_iff · cited by 0Complex.sq_nonpos_iffNoZeroDivisors · cited by 545NoZeroDivisorsMulZeroClass · cited by 232MulZeroClassmul_eq_zero_iff_rightCITED BYCITES

Cites2

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Cited by5

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