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Theorems · Theorem · order theory

Order.IsPredPrelimit.lt_pred_iff

∀ {α : Type u_1} {a b : α} [inst : PartialOrder α] [inst_1 : PredOrder α],
  Order.IsPredPrelimit b → (b < Order.pred a ↔ b < a)
Defined in
Mathlib.Order.SuccPred.Limit
Cited by
2 results in Mathlib
Foundations
Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrderPredOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Order.IsPredPrelimit.pred_le_iff · cited by 1IsPredPrelimit.pred_le_iffOrder.IsPredLimit.lt_pred_iff · cited by 0IsPredLimit.lt_pred_iffPartialOrder · cited by 6410PartialOrderPredOrder · cited by 334PredOrderOrder.pred · cited by 273Order.predOrder.IsPredPrelimit · cited by 93Order.IsPredPrelimitLE.le.trans_lt' · cited by 50le.trans_lt'Order.pred_le · cited by 19Order.pred_leOrder.IsPredPrelimit.lt_pred · cited by 4IsPredPrelimit.lt_predIsPredPrelimit.lt_pred_iffCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.