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Theorems · Theorem · order theory

monotone_of_pred_le

∀ {α : Type u_3} {β : Type u_4} [inst : PartialOrder α] [inst_1 : Preorder β] [inst_2 : PredOrder α]
  [IsPredArchimedean α] {f : α → β}, (∀ (a : α), ¬IsMin a → f (Order.pred a) ≤ f a) → Monotone f
Defined in
Mathlib.Order.SuccPred.Archimedean
Cited by
1 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrderPreorderPredOrderIsPredArchimedean
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Around this declaration

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

monotone_of_sub_one_le · cited by 0monotone_of_sub_one_lePreorder · cited by 7952PreorderPartialOrder · cited by 6410PartialOrderMonotone · cited by 1397MonotonePredOrder · cited by 334PredOrderIsMin · cited by 277IsMinOrder.pred · cited by 273Order.predIsPredArchimedean · cited by 66IsPredArchimedeanmonotoneOn_of_pred_le · cited by 3monotoneOn_of_pred_lemonotone_of_pred_leCITED BYCITES

Cites8

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Cited by1

Results whose statement or proof uses this declaration.