Theorems · Theorem · order theory

strictAntiOn_of_succ_lt

∀ {α : Type u_3} {β : Type u_4} [inst : PartialOrder α] [inst_1 : Preorder β] [inst_2 : SuccOrder α]
  [IsSuccArchimedean α] {s : Set α} {f : α → β},
  s.OrdConnected → (∀ (a : α), ¬IsMax a → a ∈ s → Order.succ a ∈ s → f (Order.succ a) < f a) → StrictAntiOn f s

Defined in

Mathlib.Order.SuccPred.Archimedean

Cited by

2 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderPreorderSuccOrderIsSuccArchimedean