Theorems · Theorem · field theory

Function.Periodic.image_Ioc

∀ {α : Type u_1} {β : Type u_2} {f : α → β} {c : α} [inst : AddCommGroup α] [inst_1 : LinearOrder α]
  [IsOrderedAddMonoid α] [Archimedean α],
  Function.Periodic f c → 0 < c → ∀ (a : α), f '' Set.Ioc a (a + c) = Set.range f

Defined in

Mathlib.Algebra.Field.Periodic

Cited by

3 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderIsOrderedAddMonoidArchimedean