Theorems · Theorem · order theory
neg_nonneg
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LE α] [AddLeftMono α] {a : α}, 0 ≤ -a ↔ a ≤ 0Alias of Left.nonneg_neg_iff.
Uses left co(ntra)variant.
- Cited by
- 60 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- AddGroupLEAddLeftMono
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
- AddLeftMonostatement · cited by 687
- Left.nonneg_neg_iffproof · cited by 14
Cited by60
Results whose statement or proof uses this declaration.
- Real.exp_posproof · cited by 169
- abs_of_nonposproof · cited by 53
- Real.rpow_le_rpow_of_nonposproof · cited by 12
- mul_self_inj_of_nonnegproof · cited by 9
- neg_nonneg_of_nonposproof · cited by 9
- Complex.ofReal_cpow_of_nonposproof · cited by 4
- AffineSubspace.wOppSide_smul_vsub_vadd_leftproof · cited by 3
- Complex.arg_of_im_negproof · cited by 3
- Zsqrtd.norm_nonnegproof · cited by 3
- jacobiTheta₂_functional_equationproof · cited by 3
- abs_nsmulproof · cited by 3
- MeasureTheory.integral_nonpos_of_aeproof · cited by 3