Theorems · Theorem · ring theory
div_neg
∀ {R : Type u_1} [inst : DivisionMonoid R] [inst_1 : HasDistribNeg R] {b : R} (a : R), a / -b = -(a / b)- Defined in
- Mathlib.Algebra.Ring.Basic
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- DivisionMonoidHasDistribNeg
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.
- DivisionMonoidstatement and proof · cited by 201
- HasDistribNegstatement and proof · cited by 114
- div_neg_eq_neg_divproof · cited by 6
Cited by22
Results whose statement or proof uses this declaration.
- IntervalIntegrable.iff_comp_negproof · cited by 6
- ProbabilityTheory.complexMGF_id_gaussianRealproof · cited by 3
- Real.tendsto_div_pow_mul_exp_add_atTopproof · cited by 3
- lt_div_iff_of_negproof · cited by 3
- le_div_iff_of_negproof · cited by 3
- HurwitzZeta.differentiableAt_hurwitzZetaEven_sub_one_divproof · cited by 3
- fourier_gaussian_pi'proof · cited by 2
- taylor_mean_remainder_lagrangeproof · cited by 1
- HurwitzZeta.jacobiTheta₂''_conjproof · cited by 1
- GaussianFourier.integral_cexp_neg_sum_mul_addproof · cited by 1
- ZetaAsymptotics.term_of_ltproof · cited by 1
- ZetaAsymptotics.term_oneproof · cited by 1