Theorems · Theorem · order theory
LinearOrderedAddCommGroupWithTop.sub_self_eq_zero_of_ne_top
∀ {α : Type u_2} [inst : LinearOrderedAddCommGroupWithTop α] {a : α}, a ≠ ⊤ → a - a = 0Alias of the reverse direction of LinearOrderedAddCommGroupWithTop.sub_self_eq_zero_iff_ne_top.
- Defined in
- Mathlib.Algebra.Order.AddGroupWithTop
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- LinearOrderedAddCommGroupWithTopstatement and proof · cited by 37
- LinearOrderedAddCommGroupWithTop.sub_self_eq_zero_iff_ne_topproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- LinearOrderedAddCommGroupWithTop.sub_posproof · cited by 1
- LinearOrderedAddCommGroupWithTop.sub_self_nonnegproof · cited by 0
- LinearOrderedAddCommGroupWithTop.sub_eq_zeroproof · cited by 0