Theorems · Theorem · order theory
subsingleton_of_top_eq_bot
∀ {α : Type u} [inst : PartialOrder α] [inst_1 : BoundedOrder α], ⊤ = ⊥ → Subsingleton α- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- PartialOrderBoundedOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- PartialOrderstatement and proof · cited by 6,410
- Bot.botstatement and proof · cited by 4,720
- le_of_eqproof · cited by 366
- BoundedOrderstatement and proof · cited by 270
- subsingleton_of_top_le_botproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- top_ne_botproof · cited by 15
- LieAlgebra.IsKilling.isLieAbelian_iff_subsingletonproof · cited by 1
- subsingleton_iff_top_eq_botproof · cited by 0