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Theorems · Theorem · order theory

Order.pred_succ_le

∀ {α : Type u_1} [inst : Preorder α] [inst_1 : PredOrder α] [inst_2 : SuccOrder α] (a : α),
  Order.pred (Order.succ a) ≤ a
Defined in
Mathlib.Order.SuccPred.Basic
Cited by
2 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderPredOrderSuccOrder
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Around this declaration

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

Order.pred_le_iff_le_succ · cited by 1Order.pred_le_iff_le_succOrder.le_succ_iff_pred_le · cited by 0Order.le_succ_iff_pred_lePreorder · cited by 7952PreorderOrder.succ · cited by 633Order.succSuccOrder · cited by 574SuccOrderPredOrder · cited by 334PredOrderOrder.pred · cited by 273Order.predOrder.wcovBy_succ · cited by 3Order.wcovBy_succWCovBy.pred_le · cited by 2WCovBy.pred_leOrder.pred_succ_leCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.