Theorems · Theorem · order theory
WithBot.isPredPrelimit_iff
∀ {α : Type u_1} [inst : Preorder α] [NoMinOrder α] {x : WithBot α},
Order.IsPredPrelimit x ↔ x = ⊥ ∨ ∃ y, x = ↑y ∧ Order.IsPredPrelimit y- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderNoMinOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- CovByproof · cited by 290
- NoMinOrderstatement and proof · cited by 247
- WithBot.recBotCoeproof · cited by 101
- Order.IsPredPrelimitstatement · cited by 93
- WithBot.coe_ne_botproof · cited by 29
- WithBot.coe_injproof · cited by 18
- WithBot.bot_ne_coeproof · cited by 12
- WithBot.forallproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- WithBot.isPredLimit_iffproof · cited by 1
- WithBot.isPredPrelimit_botproof · cited by 1