Theorems · Theorem · order theory
neg_lt_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
- 2 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_lt_iff_pos_addproof · cited by 7
- pos_add_self_iffproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- eqOn_abs_add_one_of_isMIntegralCurveOn_Iooproof · cited by 1
- le_neg_self_iffproof · cited by 1