Theorems · Theorem · order theory
neg_pos
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LT α] [AddLeftStrictMono α] {a : α}, 0 < -a ↔ a < 0Alias of Left.neg_pos_iff.
Uses left co(ntra)variant.
- Cited by
- 74 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_pos_iffproof · cited by 22
Cited by74
Results whose statement or proof uses this declaration.
- inv_lt_zero'proof · cited by 11
- Real.abs_rpow_le_abs_rpowproof · cited by 7
- Function.Periodic.intervalIntegral_add_eqproof · cited by 7
- Complex.arg_eq_pi_iffproof · cited by 7
- ENNReal.rpow_negproof · cited by 6
- integral_cexp_quadraticproof · cited by 5
- Complex.arg_mul_cos_add_sin_mul_Iproof · cited by 5
- Real.add_one_lt_expproof · cited by 4
- Int.ModEq.mul_left'proof · cited by 4
- tendsto_zpow_atTop_zeroproof · cited by 4
- Filter.tendsto_const_mul_atBot_of_negproof · cited by 3
- lt_div_iff_of_negproof · cited by 3