Theorems · Theorem · group theory
MulZeroClass.zero_mul
∀ {M₀ : Type u} [self : MulZeroClass M₀] (a : M₀), 0 * a = 0Zero is a left absorbing element for multiplication
- Defined in
- Mathlib.Algebra.GroupWithZero.Defs
- Cited by
- 1,625 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 16 definitions · uses no axioms
- Assumes
- MulZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulZeroClassstatement and proof · cited by 232
Cited by1,635
Results whose statement or proof uses this declaration.
- nsmul_eq_mulproof · cited by 369
- zero_divproof · cited by 222
- Complex.ofReal_mulproof · cited by 180
- Int.cast_mulproof · cited by 113
- sq_nonnegproof · cited by 106
- inner_zero_leftproof · cited by 59
- mul_nonneg_of_nonpos_of_nonposproof · cited by 45
- mul_pos_of_neg_of_negproof · cited by 40
- ENNReal.inv_zeroproof · cited by 37
- Polynomial.eval₂_Xproof · cited by 34
- ENNReal.rpow_mulproof · cited by 33
- Polynomial.leadingCoeff_mulproof · cited by 32
Showing the 200 most cited of 1,635.