Theorems · Theorem · group theory
mul_self_eq_zero
∀ {M₀ : Type u_1} [inst : MulZeroClass M₀] [NoZeroDivisors M₀] {a : M₀}, a * a = 0 ↔ a = 0- Defined in
- Mathlib.Algebra.GroupWithZero.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext
- Assumes
- MulZeroClassNoZeroDivisors
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
- MulZeroClassstatement and proof · cited by 232
Cited by7
Results whose statement or proof uses this declaration.
- mul_self_ne_zeroproof · cited by 3
- InnerProductGeometry.cos_angle_add_mul_norm_of_inner_eq_zeroproof · cited by 3
- CStarRing.star_mul_self_eq_zero_iffproof · cited by 2
- det_traceMatrix_ne_zero'proof · cited by 1
- quadraticChar_card_sqrtsproof · cited by 1
- mul_self_add_mul_self_eq_zeroproof · cited by 1
- IsCoercive.range_eq_topproof · cited by 0