Theorems · Theorem · order theory
eq_bot_or_bot_lt
∀ {α : Type u} [inst : PartialOrder α] [inst_1 : OrderBot α] (a : α), a = ⊥ ∨ ⊥ < a- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- Bot.botstatement · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- bot_leproof · cited by 306
- LE.le.eq_or_lt'proof · cited by 27
Cited by4
Results whose statement or proof uses this declaration.
- Order.IsSuccPrelimit.sSup_Iioproof · cited by 4
- LinearGrowth.linearGrowthSup_le_of_eventually_leproof · cited by 0
- NNReal.rpow_le_self_of_le_oneproof · cited by 0
- LinearGrowth.linearGrowthInf_le_of_eventually_leproof · cited by 0