Theorems · Theorem · order theory
LinearOrderedAddCommGroupWithTop.add_neg_cancel_iff_ne_top
∀ {α : Type u_2} [inst : LinearOrderedAddCommGroupWithTop α] {a : α}, a + -a = 0 ↔ a ≠ ⊤- Defined in
- Mathlib.Algebra.Order.AddGroupWithTop
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 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.
- Top.topstatement and proof · cited by 9,680
- add_topproof · cited by 49
- LinearOrderedAddCommGroupWithTopstatement and proof · cited by 37
- LinearOrderedAddCommGroupWithTop.add_neg_cancel_of_ne_topproof · cited by 6
- LinearOrderedAddCommGroupWithTop.neg_topproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- LinearOrderedAddCommGroupWithTop.sub_self_eq_zero_iff_ne_topproof · cited by 1