Theorems · Theorem · number theory

ThreeAPFree.of_image

∀ {α : Type u_2} {β : Type u_3} [inst : AddCommMonoid α] [inst_1 : AddCommMonoid β] {s A : Set α} {t : Set β}
  {f : α → β}, IsAddFreimanHom 2 s t f → Set.InjOn f s → A ⊆ s → ThreeAPFree (f '' A) → ThreeAPFree A

Arithmetic progressions of length three are reflected under 2-Freiman homomorphisms.

Defined in

Mathlib.Combinatorics.Additive.AP.Three.Defs

Cited by

3 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Quot.sound

Assumes

AddCommMonoidAddCommMonoid