Theorems · Theorem · ring theory
neg_inv
∀ {R : Type u_1} [inst : DivisionMonoid R] [inst_1 : HasDistribNeg R] {a : R}, -a⁻¹ = (-a)⁻¹- Defined in
- Mathlib.Algebra.Ring.Basic
- Cited by
- 11 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.
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
- HasDistribNegstatement and proof · cited by 114
- inv_eq_one_divproof · cited by 33
- div_neg_eq_neg_divproof · cited by 6
Cited by11
Results whose statement or proof uses this declaration.
- inv_negproof · cited by 42
- hasSum_geometric_of_lt_oneproof · cited by 14
- slope_commproof · cited by 9
- hasSum_geometric_of_norm_lt_oneproof · cited by 4
- AkraBazziRecurrence.isLittleO_deriv_smoothingFnproof · cited by 2
- LocallyIntegrable.ae_hasDerivAt_integralproof · cited by 1
- Pell.Solution₁.exists_pos_variantproof · cited by 1
- inv_neg_oneproof · cited by 1
- le_rpow_one_add_norm_iff_norm_leproof · cited by 1
- Real.inv_goldenConjproof · cited by 1
- PeriodPair.G_eq_zero_of_oddproof · cited by 0