Theorems · Theorem · order theory
LinearOrderedAddCommGroupWithTop.neg_pos
∀ {α : Type u_2} [inst : LinearOrderedAddCommGroupWithTop α] {a : α}, 0 < -a ↔ a < 0 ∨ a = ⊤- Defined in
- Mathlib.Algebra.Order.AddGroupWithTop
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- zero_subproof · cited by 335
- LinearOrderedAddCommGroupWithTopstatement and proof · cited by 37
- LinearOrderedAddCommGroupWithTop.sub_posproof · cited by 1
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