Theorems · Theorem · group theory
neg_ne_zero
∀ {α : Type u_1} [inst : SubtractionMonoid α] {a : α}, -a ≠ 0 ↔ a ≠ 0- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 70 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- SubtractionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Iff.notproof · cited by 489
- SubtractionMonoidstatement and proof · cited by 208
- neg_eq_zeroproof · cited by 171
Cited by70
Results whose statement or proof uses this declaration.
- IntervalIntegrable.iff_comp_negproof · cited by 6
- Orientation.eq_or_eq_neg_of_isEmptyproof · cited by 6
- Real.Angle.neg_pi_div_two_ne_zeroproof · cited by 6
- Projectivization.mk_eq_mk_iff_crossProduct_eq_zeroproof · cited by 5
- quadraticChar_neg_oneproof · cited by 5
- Complex.Gamma_neg_nat_eq_zeroproof · cited by 4
- Complex.ofReal_cpow_of_nonposproof · cited by 4
- AbsoluteValue.map_negproof · cited by 4
- intervalIntegral.integral_comp_sub_mulproof · cited by 3
- Function.support_fun_negproof · cited by 3
- HasDerivAt.lhopital_zero_atTop_on_Ioiproof · cited by 3
- Module.Ray.ne_neg_selfproof · cited by 3