Theorems · Theorem · order theory
neg_pos_of_neg
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LT α] [AddLeftStrictMono α] {a : α}, a < 0 → 0 < -aAlias of the reverse direction of Left.neg_pos_iff.
Uses left co(ntra)variant.
- Cited by
- 13 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 and proof · cited by 4,410
- AddLeftStrictMonostatement and proof · cited by 203
- Left.neg_pos_iffproof · cited by 22
Cited by13
Results whose statement or proof uses this declaration.
- Orientation.oangle_smul_right_of_negproof · cited by 7
- Orientation.oangle_smul_left_of_negproof · cited by 5
- eq_zero_of_neg_eqproof · cited by 4
- smul_lt_smul_iff_of_neg_leftproof · cited by 4
- Real.sin_sq_lt_sqproof · cited by 3
- InnerProductGeometry.angle_smul_right_of_negproof · cited by 2
- smul_le_smul_iff_of_neg_leftproof · cited by 2
- EReal.induction₂_neg_leftproof · cited by 2
- EReal.induction₂_symm_negproof · cited by 2
- smul_lt_smul_of_neg_leftproof · cited by 1
- AbsoluteValue.IsEquiv.log_div_log_posproof · cited by 1
- EuclideanGeometry.angle_eq_zero_of_angle_eq_pi_leftproof · cited by 1