Theorems · Theorem · order theory
sign_neg
∀ {α : Type u_1} [inst : Zero α] [inst_1 : Preorder α] [inst_2 : DecidableLT α] {a : α}, a < 0 → SignType.sign a = -1- Defined in
- Mathlib.Data.Sign.Defs
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ZeroPreorderDecidableLT
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.
- DFunLike.coestatement · cited by 62,936
- Preorderstatement and proof · cited by 7,952
- OrderHomstatement · cited by 934
- SignTypestatement and proof · cited by 318
- SignType.signstatement · cited by 128
- asymmproof · cited by 12
- sign_applyproof · cited by 5
Cited by35
Results whose statement or proof uses this declaration.
- sign_mulproof · cited by 11
- sign_eq_neg_one_iffproof · cited by 9
- Affine.Simplex.ExcenterExists.dist_excenterproof · cited by 6
- EReal.sign_mul_absproof · cited by 3
- Affine.Simplex.sSameSide_affineSpan_faceOpposite_of_sign_eqproof · cited by 3
- Affine.Simplex.sign_excenterWeights_singleton_negproof · cited by 3
- self_mul_signproof · cited by 3
- hasStrictDerivAt_absproof · cited by 2
- EuclideanGeometry.oangle_swap₁₂_signproof · cited by 2
- Affine.Simplex.sOppSide_affineSpan_faceOpposite_iffproof · cited by 2
- Affine.Simplex.sSameSide_affineSpan_faceOpposite_iffproof · cited by 2
- sign_mul_absproof · cited by 2