Theorems · Theorem · ring theory
neg_eq_neg_one_mul
∀ {α : Type u} [inst : MulOneClass α] [inst_1 : HasDistribNeg α] (a : α), -a = -1 * a- Defined in
- Mathlib.Algebra.Ring.Defs
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext
- Assumes
- MulOneClassHasDistribNeg
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- one_mulproof · cited by 2,841
- MulOneClassstatement and proof · cited by 1,018
- neg_mulproof · cited by 654
- HasDistribNegstatement and proof · cited by 114
Cited by21
Results whose statement or proof uses this declaration.
- neg_divproof · cited by 161
- Complex.cos_eq_zero_iffproof · cited by 5
- IsPrimitiveRoot.sub_one_norm_eq_eval_cyclotomicproof · cited by 3
- jacobiSum_mul_nontrivialproof · cited by 3
- hasSum_one_div_nat_pow_mul_fourierproof · cited by 2
- hasSum_one_div_nat_pow_mul_sinproof · cited by 2
- Polynomial.reflect_negproof · cited by 2
- Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegreeproof · cited by 1
- IsPrimitiveRoot.exists_neg_pow_of_isOfFinOrderproof · cited by 1
- MvPolynomial.mul_esymm_eq_sumproof · cited by 1
- Complex.cos_ne_zero_of_arctan_boundsproof · cited by 1
- Algebra.discr_powerBasis_eq_prod''proof · cited by 1