Theorems · Theorem · order theory
sign_zero
∀ {α : Type u_1} [inst : Zero α] [inst_1 : Preorder α] [inst_2 : DecidableLT α], SignType.sign 0 = 0- Defined in
- Mathlib.Data.Sign.Defs
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 64 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.
Cites5
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 · cited by 318
- SignType.signstatement · cited by 128
Cited by33
Results whose statement or proof uses this declaration.
- sign_mulproof · cited by 11
- Real.Angle.sign_zeroproof · cited by 9
- Affine.Simplex.sSameSide_affineSpan_faceOpposite_of_sign_eqproof · cited by 3
- sign_eq_zero_iffproof · cited by 3
- self_mul_signproof · cited by 3
- Real.Angle.sign_coe_piproof · cited by 2
- sign_mul_absproof · cited by 2
- fderiv_norm_smulproof · cited by 2
- Orientation.oangle_sign_smul_rightproof · cited by 2
- eventually_nhdsWithin_sign_eq_of_deriv_posproof · cited by 2
- Polynomial.signVariations_eq_eraseLead_add_iteproof · cited by 1
- NormedSpace.normalize_smulproof · cited by 1