Theorems · Theorem · number theory

IsMulFreimanHom.mulRothNumber_mono

∀ {α : Type u_2} {β : Type u_3} [inst : DecidableEq α] [inst_1 : CommMonoid α] [inst_2 : CommMonoid β]
  [inst_3 : DecidableEq β] {A : Finset α} {B : Finset β} {f : α → β},
  IsMulFreimanHom 2 (↑A) (↑B) f → Set.BijOn f ↑A ↑B → mulRothNumber B ≤ mulRothNumber A

Arithmetic progressions can be pushed forward along bijective 2-Freiman homs.

Defined in

Mathlib.Combinatorics.Additive.AP.Three.Defs

Cited by

1 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqCommMonoidCommMonoidDecidableEq