Theorems · Theorem · order theory
Left.nonneg_neg_iff
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LE α] [AddLeftMono α] {a : α}, 0 ≤ -a ↔ a ≤ 0Uses 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_nonnegproof · cited by 60
- max_zero_sub_max_neg_zero_eq_selfproof · cited by 6
- nonpos_of_neg_nonnegproof · cited by 3
- negPart_eq_negproof · cited by 3
- wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonnegproof · cited by 2
- le_sub_self_iffproof · cited by 2
- MeasureTheory.SignedMeasure.toJordanDecomposition_smul_realproof · cited by 1
- max_zero_add_max_neg_zero_eq_abs_selfproof · cited by 1
- DivisibleHull.qsmul_mkproof · cited by 1
- DivisibleHull.qsmul_of_nonposstatement and proof · cited by 1
- wbtw_smul_vadd_smul_vadd_of_nonpos_of_leproof · cited by 1
- AddSubgroup.isLeast_of_closure_iff_eq_absproof · cited by 0