Theorems · Theorem · order theory
WithBot.isSuccPrelimit_iff
∀ {α : Type u_1} [inst : Preorder α] {x : WithBot α}, Order.IsSuccPrelimit x ↔ x = ⊥ ∨ ∃ y, x = ↑y ∧ Order.IsSuccLimit y- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Order.IsSuccLimitstatement and proof · cited by 255
- Order.IsSuccPrelimitstatement · cited by 157
- WithBot.recBotCoeproof · cited by 101
- WithBot.coe_ne_botproof · cited by 29
- not_isMin_iffproof · cited by 18
- WithBot.coe_injproof · cited by 18
- WithBot.bot_ne_coeproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- Order.IsSuccLimit.withBotCoeproof · cited by 0