Theorems · Theorem · order theory

strictMonoOn_Ici_of_pred_lt

∀ {α : Type u_1} {β : Type u_2} [inst : PartialOrder α] [inst_1 : Preorder β] {ψ : α → β} [inst_2 : PredOrder α]
  [IsPredArchimedean α] {n : α}, (∀ (m : α), n < m → ψ (Order.pred m) < ψ m) → StrictMonoOn ψ (Set.Ici n)

Defined in

Mathlib.Order.Interval.Set.Monotone

Cited by

0 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderPreorderPredOrderIsPredArchimedean