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Theorems · Theorem · order theory

Order.bot_lt_succ

∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : SuccOrder α] [inst_2 : OrderBot α] [Nontrivial α] (a : α),
  ⊥ < Order.succ a
Defined in
Mathlib.Order.SuccPred.Basic
Cited by
1 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrderSuccOrderOrderBotNontrivial
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Order.succ_ne_bot · cited by 2Order.succ_ne_botPartialOrder · cited by 6410PartialOrderBot.bot · cited by 4720Bot.botNontrivial · cited by 2416NontrivialOrderBot · cited by 1055OrderBotLT.lt.trans_le · cited by 678lt.trans_leOrder.succ · cited by 633Order.succSuccOrder · cited by 574SuccOrderbot_le · cited by 306bot_leOrder.lt_succ_of_not_isMax · cited by 25Order.lt_succ_of_not_isMaxOrder.succ_le_succ · cited by 7Order.succ_le_succnot_isMax_bot · cited by 1not_isMax_botOrder.bot_lt_succCITED BYCITES

Cites11

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.