Theorems · Theorem · order theory
sign_mul
∀ {α : Type u} [inst : Ring α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] (x y : α),
SignType.sign (x * y) = SignType.sign x * SignType.sign y- Defined in
- Mathlib.Data.Sign.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- mul_oneproof · cited by 3,885
- IsStrictOrderedRingstatement and proof · cited by 2,490
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- neg_negproof · cited by 960
- OrderHomstatement · cited by 934
- mul_negproof · cited by 590
- neg_zeroproof · cited by 542
- SignTypestatement · cited by 318
Cited by12
Results whose statement or proof uses this declaration.
- signHomproof · cited by 4
- Affine.Simplex.ExcenterExists.sign_touchpointWeightsproof · cited by 4
- Affine.Simplex.sign_excenterWeights_singleton_negproof · cited by 3
- Affine.Simplex.sign_excenterWeights_singleton_posproof · cited by 3
- Real.Angle.sign_two_nsmul_eq_sign_iffproof · cited by 2
- Affine.Simplex.ExcenterExists.sign_signedInfDist_excenterproof · cited by 2
- Affine.Simplex.ExcenterExists.excenterWeights_eq_excenterWeights_iffproof · cited by 1
- sign_eq_of_affineCombination_mem_affineSpan_pairproof · cited by 1
- Polynomial.succ_signVariations_X_sub_C_mul_monomialproof · cited by 0
- Orientation.oangle_sign_smul_add_smul_smul_add_smulproof · cited by 0
- EReal.sign_mulproof · cited by 0
- Polynomial.signVariations_C_mulproof · cited by 0