Theorems · Theorem · order theory
Left.neg_neg_iff
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LT α] [AddLeftStrictMono α] {a : α}, -a < 0 ↔ 0 < aUses left co(ntra)variant.
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- AddGroupLTAddLeftStrictMono
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.
- AddGroupstatement and proof · cited by 4,410
- add_zeroproof · cited by 2,707
- add_neg_cancelproof · cited by 213
- AddLeftStrictMonostatement and proof · cited by 203
- add_lt_add_iff_leftproof · cited by 30
Cited by16
Results whose statement or proof uses this declaration.
- neg_lt_zeroproof · cited by 36
- Real.Angle.toReal_zeroproof · cited by 10
- sub_lt_self_iffproof · cited by 8
- Sbtw.angle₁₂₃_eq_piproof · cited by 6
- Complex.arg_neg_coe_angleproof · cited by 3
- Complex.arg_neg_eq_arg_sub_pi_of_im_posproof · cited by 3
- Left.neg_lt_selfproof · cited by 3
- neg_neg_iff_posproof · cited by 2
- LinearOrderedAddCommGroup.Subgroup.exists_neg_generatorproof · cited by 2
- AffineSubspace.setOfPred_sOppSide_eq_image2proof · cited by 2
- AffineSubspace.setOfPred_wOppSide_eq_image2proof · cited by 2
- Real.Angle.abs_toReal_coe_eq_self_iffproof · cited by 1