Theorems · Theorem · order theory

monotoneOn_of_pred_le

∀ {α : Type u_3} {β : Type u_4} [inst : PartialOrder α] [inst_1 : Preorder β] [inst_2 : PredOrder α]
  [IsPredArchimedean α] {s : Set α} {f : α → β},
  s.OrdConnected → (∀ (a : α), ¬IsMin a → a ∈ s → Order.pred a ∈ s → f (Order.pred a) ≤ f a) → MonotoneOn f s

Defined in

Mathlib.Order.SuccPred.Archimedean

Cited by

3 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderPreorderPredOrderIsPredArchimedean