Theorems · Theorem · order theory

strictMonoOn_of_lt_add_one

∀ {α : Type u_2} {β : Type u_3} [inst : PartialOrder α] [inst_1 : Preorder β] [inst_2 : Add α] [inst_3 : One α]
  [inst_4 : SuccAddOrder α] [IsSuccArchimedean α] {s : Set α} {f : α → β},
  s.OrdConnected → (∀ (a : α), ¬IsMax a → a ∈ s → a + 1 ∈ s → f a < f (a + 1)) → StrictMonoOn f s

Defined in

Mathlib.Algebra.Order.SuccPred

Cited by

3 results in Mathlib

Foundations

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

Assumes

PartialOrderPreorderAddOneSuccAddOrderIsSuccArchimedean