Theorems · Theorem · order theory

Monotone.biUnion_Ico_Ioc_map_succ

∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : SuccOrder α] [IsSuccArchimedean α]
  [inst_3 : LinearOrder β] {f : α → β},
  Monotone f → ∀ (m n : α), ⋃ i ∈ Set.Ico m n, Set.Ioc (f i) (f (Order.succ i)) = Set.Ioc (f m) (f n)

If α is a linear archimedean succ order and β is a linear order, then for any monotone function f and m n : α, the union of intervals Set.Ioc (f i) (f (Order.succ i)), m ≤ i < n, is equal to Set.Ioc (f m) (f n)

Defined in

Mathlib.Order.SuccPred.IntervalSucc

Cited by

0 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderSuccOrderIsSuccArchimedeanLinearOrder