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Theorems · Theorem · order theory

Order.IsSuccPrelimit.succ_lt_iff

∀ {α : Type u_1} {a b : α} [inst : PartialOrder α] [inst_1 : SuccOrder α],
  Order.IsSuccPrelimit b → (Order.succ a < b ↔ a < b)
Defined in
Mathlib.Order.SuccPred.Limit
Cited by
2 results in Mathlib
Foundations
Depth 15 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.IsSuccLimit.succ_lt_iff · cited by 2IsSuccLimit.succ_lt_iffOrder.IsSuccPrelimit.le_succ_iff · cited by 2IsSuccPrelimit.le_succ_iffPartialOrder · cited by 6410PartialOrderLE.le.trans_lt · cited by 795le.trans_ltOrder.succ · cited by 633Order.succSuccOrder · cited by 574SuccOrderOrder.IsSuccPrelimit · cited by 157Order.IsSuccPrelimitOrder.le_succ · cited by 96Order.le_succOrder.IsSuccPrelimit.succ_lt · cited by 7IsSuccPrelimit.succ_ltIsSuccPrelimit.succ_lt_iffCITED 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.