Theorems · Theorem · order theory
bot_lt_top
∀ {α : Type u} [inst : PartialOrder α] [inst_1 : BoundedOrder α] [Nontrivial α], ⊥ < ⊤- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- Bot.botstatement · cited by 4,720
- Nontrivialstatement and proof · cited by 2,416
- BoundedOrderstatement and proof · cited by 270
- lt_top_iff_ne_topproof · cited by 95
- bot_ne_topproof · cited by 24
Cited by7
Results whose statement or proof uses this declaration.
- EReal.neg_strictAntiproof · cited by 2
- Finset.sup_eq_top_iffproof · cited by 2
- IsSimpleOrder.bot_lt_iff_eq_topproof · cited by 1
- MeasureTheory.SimpleFunc.eapprox_lt_topproof · cited by 1
- Finset.inf_eq_bot_iffproof · cited by 1
- IsSimpleOrder.lt_top_iff_eq_botproof · cited by 0
- SignType.neg_one_lt_oneproof · cited by 0