Theorems · Theorem · order theory
neg_lt_zero
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LT α] [AddLeftStrictMono α] {a : α}, -a < 0 ↔ 0 < aAlias of Left.neg_neg_iff.
Uses left co(ntra)variant.
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- AddGroupLTAddLeftStrictMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement · cited by 4,410
- AddLeftStrictMonostatement · cited by 203
- Left.neg_neg_iffproof · cited by 16
Cited by36
Results whose statement or proof uses this declaration.
- neg_one_lt_zeroproof · cited by 14
- UpperHalfPlane.norm_qParam_lt_oneproof · cited by 5
- summable_jacobiTheta₂_term_iffproof · cited by 4
- AbsoluteValue.map_negproof · cited by 4
- Complex.differentiable_one_div_Gammaproof · cited by 4
- TFAE_exists_lt_isLittleO_powproof · cited by 4
- eq_zero_of_neg_eqproof · cited by 4
- Function.Periodic.invQParam_tendstoproof · cited by 3
- Complex.tsum_exp_neg_quadraticproof · cited by 3
- Real.arcsin_nonnegproof · cited by 3
- ZMod.valMinAbs_mem_Iocproof · cited by 3
- IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_dvdproof · cited by 3