Theorems · Theorem · ring theory
neg_div
∀ {R : Type u_1} [inst : DivisionMonoid R] [inst_1 : HasDistribNeg R] (a b : R), -b / a = -(b / a)- Defined in
- Mathlib.Algebra.Ring.Basic
- Cited by
- 161 results in Mathlib
- Foundations
- Depth 8 from the axioms, rests on 48 definitions · uses propext
- Assumes
- DivisionMonoidHasDistribNeg
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.
- DivisionMonoidstatement and proof · cited by 201
- mul_div_assocproof · cited by 149
- HasDistribNegstatement and proof · cited by 114
- neg_eq_neg_one_mulproof · cited by 21
Cited by161
Results whose statement or proof uses this declaration.
- Rat.cast_negproof · cited by 25
- neg_div_neg_eqproof · cited by 17
- Complex.sin_negproof · cited by 17
- div_sub_div_sameproof · cited by 11
- UpperHalfPlane.modular_S_smulproof · cited by 9
- Complex.cos_argproof · cited by 7
- UpperHalfPlane.im_inv_neg_coe_posproof · cited by 7
- InnerProductGeometry.angle_neg_rightproof · cited by 7
- Complex.sinh_negproof · cited by 6
- Real.arctan_negproof · cited by 6
- neg_div'proof · cited by 5
- HurwitzZeta.hurwitzZetaOdd_negproof · cited by 5