Theorems · Theorem · order theory
Left.neg_nonpos_iff
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LE α] [AddLeftMono α] {a : α}, -a ≤ 0 ↔ 0 ≤ aUses left co(ntra)variant.
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- AddGroupLEAddLeftMono
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
- AddLeftMonostatement and proof · cited by 687
- add_neg_cancelproof · cited by 213
- add_le_add_iff_leftproof · cited by 45
Cited by14
Results whose statement or proof uses this declaration.
- neg_nonposproof · cited by 31
- sub_le_self_iffproof · cited by 7
- max_zero_sub_max_neg_zero_eq_selfproof · cited by 6
- negPart_eq_zeroproof · cited by 4
- wbtw_swap_left_iffproof · cited by 2
- Real.arccos_eq_arcsinproof · cited by 2
- max_zero_add_max_neg_zero_eq_abs_selfproof · cited by 1
- Left.neg_le_selfproof · cited by 1
- nonneg_of_neg_nonposproof · cited by 1
- ArchimedeanClass.pos_of_pos_of_mk_ltproof · cited by 1
- tendsto_integral_mul_one_add_inv_smul_sq_powproof · cited by 1
- Real.abs_mulExpNegMulSq_comp_le_normproof · cited by 1