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Theorems · Theorem · order theory

Order.lt_succ_bot_iff

∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : SuccOrder α] {a : α} [inst_2 : OrderBot α] [NoMaxOrder α],
  a < Order.succ ⊥ ↔ a = ⊥
Defined in
Mathlib.Order.SuccPred.Basic
Cited by
1 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderSuccOrderOrderBotNoMaxOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cardinal.lt_one_iff · cited by 5Cardinal.lt_one_iffLinearOrder · cited by 8572LinearOrderBot.bot · cited by 4720Bot.botOrderBot · cited by 1055OrderBotOrder.succ · cited by 633Order.succSuccOrder · cited by 574SuccOrderNoMaxOrder · cited by 340NoMaxOrderle_bot_iff · cited by 116le_bot_iffOrder.lt_succ_iff · cited by 22Order.lt_succ_iffOrder.lt_succ_bot_iffCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.