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Theorems · Theorem · order theory

Order.isSuccLimit_iff_of_orderBot

∀ {α : Type u_1} {a : α} [inst : PartialOrder α] [inst_1 : OrderBot α],
  Order.IsSuccLimit a ↔ a ≠ ⊥ ∧ Order.IsSuccPrelimit a
Defined in
Mathlib.Order.SuccPred.Limit
Cited by
2 results in Mathlib
Foundations
Depth 8 from the axioms · uses propext
Assumes
PartialOrderOrderBot
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Ordinal.isSuccLimit_iff · cited by 6Ordinal.isSuccLimit_iffCardinal.isSuccLimit_iff · cited by 3Cardinal.isSuccLimit_iffPartialOrder · cited by 6410PartialOrderBot.bot · cited by 4720Bot.botOrderBot · cited by 1055OrderBotOrder.IsSuccLimit · cited by 255Order.IsSuccLimitOrder.IsSuccPrelimit · cited by 157Order.IsSuccPrelimitOrder.isSuccLimit_iff · cited by 9Order.isSuccLimit_iffisMin_iff_eq_bot · cited by 7isMin_iff_eq_botOrder.isSuccLimit_iff_of_orde…CITED BYCITES

Cites7

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

Cited by2

Results whose statement or proof uses this declaration.