Theorems · Theorem · ring theory
neg_mul_neg
∀ {α : Type u} [inst : Mul α] [inst_1 : HasDistribNeg α] (a b : α), -a * -b = a * b- Defined in
- Mathlib.Algebra.Ring.Defs
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext
- Assumes
- MulHasDistribNeg
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.
- neg_negproof · cited by 960
- neg_mulproof · cited by 654
- mul_negproof · cited by 590
- HasDistribNegstatement and proof · cited by 114
Cited by32
Results whose statement or proof uses this declaration.
- abs_mul_abs_selfproof · cited by 21
- jacobiTheta₂_neg_leftproof · cited by 7
- Real.arctan_addproof · cited by 6
- Ideal.span_singleton_negproof · cited by 5
- IsEllipticNet.atom_neg_leftproof · cited by 4
- AbsoluteValue.map_negproof · cited by 4
- spectrum.subset_polynomial_aevalproof · cited by 4
- Hyperreal.infinitePos_mul_of_infiniteNeg_not_infinitesimal_negproof · cited by 3
- one_div_neg_one_eq_neg_oneproof · cited by 3
- IsCoprime.neg_leftproof · cited by 3
- discrim_le_zeroproof · cited by 3
- ZNum.mul_to_intproof · cited by 2