Theorems · Theorem · order theory
WithBot.isPredLimit_iff
∀ {α : Type u_1} [inst : Preorder α] [Nonempty α] [NoMinOrder α] {x : WithBot α},
Order.IsPredLimit x ↔ x = ⊥ ∨ ∃ y, x = ↑y ∧ Order.IsPredLimit y- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderNonemptyNoMinOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Bot.botstatement and proof · cited by 4,720
- WithBotstatement and proof · cited by 1,498
- WithBot.somestatement and proof · cited by 541
- NoMinOrderstatement and proof · cited by 247
- WithBot.recBotCoeproof · cited by 101
- Order.IsPredPrelimitproof · cited by 93
- Order.IsPredLimitstatement · cited by 60
- WithBot.coe_lt_coeproof · cited by 55
- lt_self_iff_falseproof · cited by 41
- WithBot.bot_lt_coeproof · cited by 37
- WithBot.coe_ne_botproof · cited by 29
Cited by1
Results whose statement or proof uses this declaration.
- WithBot.isPredLimit_botproof · cited by 0