Theorems · Theorem · group theory
eq_zero_of_mul_self_eq_zero
∀ {M₀ : Type u_1} [inst : Mul M₀] [inst_1 : Zero M₀] [NoZeroDivisors M₀] {a : M₀}, a * a = 0 → a = 0- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- MulZeroNoZeroDivisors
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.
- NoZeroDivisorsstatement and proof · cited by 545
- NoZeroDivisors.eq_zero_or_eq_zero_of_mul_eq_zeroproof · cited by 14
Cited by2
Results whose statement or proof uses this declaration.
- Zsqrtd.norm_eq_zeroproof · cited by 1
- Zsqrtd.norm_eq_zero_iffproof · cited by 0