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Theorems · Theorem · order theory

Order.isSuccPrelimit_of_succ_lt

∀ {α : Type u_1} {b : α} [inst : PartialOrder α] [inst_1 : SuccOrder α],
  (∀ a < b, Order.succ a < b) → Order.IsSuccPrelimit b
Defined in
Mathlib.Order.SuccPred.Limit
Cited by
3 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrderSuccOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Order.isSuccPrelimit_iff_succ_lt · cited by 4Order.isSuccPrelimit_iff_…Cardinal.isSuccPrelimit_aleph0 · cited by 1Cardinal.isSuccPrelimit_a…Cardinal.IsStrongPrelimit.isSuccPrelimit · cited by 1IsStrongPrelimit.isSuccPr…PartialOrder · cited by 6410PartialOrderLT.lt.ne · cited by 872lt.neOrder.succ · cited by 633Order.succSuccOrder · cited by 574SuccOrderCovBy · cited by 290CovByOrder.IsSuccPrelimit · cited by 157Order.IsSuccPrelimitCovBy.lt · cited by 51CovBy.ltCovBy.succ_eq · cited by 8CovBy.succ_eqOrder.isSuccPrelimit_of_succ_…CITED BYCITES

Cites8

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

Cited by3

Results whose statement or proof uses this declaration.