Theorems · Theorem · ring theory
div_neg_eq_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
- 6 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- DivisionMonoidHasDistribNeg
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- mul_one_divproof · cited by 45
- inv_eq_one_divproof · cited by 33
- division_defproof · cited by 21
- neg_mul_eq_mul_negproof · cited by 15
- one_div_neg_eq_neg_one_divproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- div_negproof · cited by 22
- neg_div_neg_eqproof · cited by 17
- neg_invproof · cited by 11
- real_inner_div_norm_mul_norm_eq_neg_one_of_ne_zero_of_neg_mulproof · cited by 0
- Asymptotics.IsLittleO.of_tendsto_div_atBotproof · cited by 0
- div_neg_selfproof · cited by 0