Theorems · Theorem · order theory
sign_eq_neg_one_iff
∀ {α : Type u_1} [inst : Zero α] [inst_1 : Preorder α] [inst_2 : DecidableLT α] {a : α}, SignType.sign a = -1 ↔ a < 0- Defined in
- Mathlib.Data.Sign.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 66 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.
Cites8
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
- Preorderstatement and proof · cited by 7,952
- OrderHomstatement · cited by 934
- SignTypestatement and proof · cited by 318
- SignType.signstatement and proof · cited by 128
- sign_negproof · cited by 35
- SignType.ctorIdxproof · cited by 11
- sign_applyproof · cited by 5
Cited by9
Results whose statement or proof uses this declaration.
- Affine.Simplex.sSameSide_affineSpan_faceOpposite_of_sign_eqproof · cited by 3
- Real.Angle.toReal_neg_iff_sign_negproof · cited by 2
- Affine.Simplex.sOppSide_affineSpan_faceOpposite_iffproof · cited by 2
- Affine.Simplex.sSameSide_affineSpan_faceOpposite_iffproof · cited by 2
- deriv_neg_right_of_sign_derivproof · cited by 1
- Affine.Simplex.sOppSide_excenter_singleton_pointproof · cited by 1
- Affine.Simplex.sOppSide_point_excenter_singletonproof · cited by 1
- Affine.Simplex.wOppSide_affineSpan_faceOpposite_iffproof · cited by 1
- deriv_neg_left_of_sign_derivproof · cited by 0