Theorems · Theorem · combinatorics

IsAddFreimanHom.sum_apply

∀ {α : Type u_2} {β : Type u_3} [inst : AddCommMonoid α] [inst_1 : AddCommMonoid β] {A : Set α} {B : Set β} {f : α → β}
  {n : ℕ},
  IsAddFreimanHom n A B f →
    ∀ {s t : Finset α} {hsA : ↑s ⊆ A} {htA : ↑t ⊆ A},
      s.card = n → t.card = n → ∑ i ∈ s, i = ∑ i ∈ t, i → ∑ i ∈ s, f i = ∑ i ∈ t, f i

A version of the Freiman homomorphism condition expressed using Finsets, for practicality.

Defined in

Mathlib.Combinatorics.Additive.FreimanHom

Cited by

0 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidAddCommMonoid