Theorems · Theorem · order theory
LinearOrderedAddCommGroupWithTop.add_neg_cancel_of_ne_top
∀ {α : Type u_3} [self : LinearOrderedAddCommGroupWithTop α] ⦃x : α⦄, x ≠ ⊤ → x + -x = 0- Defined in
- Mathlib.Algebra.Order.AddGroupWithTop
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- AddMonoid.toZerostatement · cited by 325
- LinearOrderedAddCommGroupWithTopstatement and proof · cited by 37
- LinearOrderedAddCommGroupWithTop.toNegstatement · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- LinearOrderedAddCommGroupWithTop.neg_add_cancel_of_ne_topproof · cited by 2
- LinearOrderedAddCommGroupWithTop.add_neg_cancel_iff_ne_topproof · cited by 1
- LinearOrderedAddCommGroupWithTop.isAddUnit_iffproof · cited by 0
- LinearOrderedAddCommGroupWithTop.neg_eq_topproof · cited by 0
- LinearOrderedAddCommGroupWithTop.add_neg_cancel_left_of_ne_topproof · cited by 0
- LinearOrderedAddCommGroupWithTop.add_neg_cancel_right_of_ne_topproof · cited by 0