Theorems · Theorem · order theory
Left.sign_neg
∀ {α : Type u_1} [inst : AddGroup α] [inst_1 : Preorder α] [inst_2 : DecidableLT α] [AddLeftStrictMono α] (a : α),
SignType.sign (-a) = -SignType.sign a- Defined in
- Mathlib.Data.Sign.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- AddGroupstatement and proof · cited by 4,410
- neg_negproof · cited by 960
- OrderHomstatement · cited by 934
- neg_zeroproof · cited by 542
- SignTypestatement · cited by 318
- AddLeftStrictMonostatement and proof · cited by 203
- SignType.signstatement · cited by 128
- lt_asymmproof · cited by 16
- SignType.ctorIdxproof · cited by 11
Cited by9
Results whose statement or proof uses this declaration.
- Real.Angle.sign_negproof · cited by 15
- Real.Angle.sign_antiperiodicproof · cited by 3
- EReal.sign_negproof · cited by 1
- HurwitzZeta.hasSum_nat_hurwitzZetaOddproof · cited by 1
- isLocalMin_of_sign_derivproof · 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
- eventually_nhdsWithin_sign_eq_of_deriv_negproof · cited by 0
- Real.Angle.sign_coe_neg_pi_div_twoproof · cited by 0