Theorems · Theorem · order theory
subsingleton_of_top_le_bot
∀ {α : Type u} [inst : PartialOrder α] [inst_1 : BoundedOrder α], ⊤ ≤ ⊥ → Subsingleton α- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- PartialOrderBoundedOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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_antisymmproof · cited by 2,068
- le_transproof · cited by 985
- le_topproof · cited by 411
- bot_leproof · cited by 306
- BoundedOrderstatement and proof · cited by 270
Cited by2
Results whose statement or proof uses this declaration.
- subsingleton_of_bot_eq_topproof · cited by 8
- subsingleton_of_top_eq_botproof · cited by 3