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Theorems · Theorem · order theory

Order.IsSuccPrelimit.le_succ_iff

∀ {α : Type u_1} {a b : α} [inst : LinearOrder α] [inst_1 : SuccOrder α],
  Order.IsSuccPrelimit b → (b ≤ Order.succ a ↔ b ≤ a)
Defined in
Mathlib.Order.SuccPred.Limit
Cited by
2 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderSuccOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Order.IsSuccLimit.le_succ_iff · cited by 1IsSuccLimit.le_succ_iffOrdinal.pred_le_iff_le_succ · cited by 1Ordinal.pred_le_iff_le_su…LinearOrder · cited by 8572LinearOrderOrder.succ · cited by 633Order.succSuccOrder · cited by 574SuccOrderOrder.IsSuccPrelimit · cited by 157Order.IsSuccPrelimitle_iff_le_iff_lt_iff_lt · cited by 25le_iff_le_iff_lt_iff_ltOrder.IsSuccPrelimit.succ_lt_iff · cited by 2IsSuccPrelimit.succ_lt_iffIsSuccPrelimit.le_succ_iffCITED BYCITES

Cites6

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.