Theorems · Theorem · ring theory
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
- 590 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 13 definitions · uses no axioms
- Assumes
- MulHasDistribNeg
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- HasDistribNegstatement and proof · cited by 114
- HasDistribNeg.mul_negproof · cited by 1
Cited by590
Results whose statement or proof uses this declaration.
- abs_mulproof · cited by 98
- Real.rpow_negproof · cited by 36
- neg_mul_negproof · cited by 32
- neg_sqproof · cited by 31
- mul_neg_oneproof · cited by 30
- dvd_negproof · cited by 19
- Complex.cpow_negproof · cited by 17
- Real.cos_antiperiodicproof · cited by 16
- neg_mul_eq_mul_negproof · cited by 15
- Odd.neg_powproof · cited by 14
- Real.sin_antiperiodicproof · cited by 14
- Polynomial.div_modByMonic_uniqueproof · cited by 12
Showing the 200 most cited of 590.