Theorems · Theorem · order theory
neg_le_self_iff
∀ {α : Type u} [inst : AddCommGroup α] [inst_1 : LinearOrder α] [IsOrderedAddMonoid α] {a : α}, -a ≤ a ↔ 0 ≤ a- Defined in
- Mathlib.Algebra.Order.Group.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- neg_le_iff_add_nonneg'proof · cited by 3
- nonneg_add_self_iffproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- abs_eq_selfproof · cited by 59
- MeasureTheory.isTightMeasureSet_of_tendsto_charFunproof · cited by 1
- AddSubgroup.isLeast_of_closure_iff_eq_absproof · cited by 0
- lt_neg_self_iffproof · cited by 0