Prove that a nonempty subset AAA of VVV is an affine subset of VVV if and only if λv+(1−λ)w∈A\lambda v + (1-\lambda)w \in Aλv+(1−λ)w∈A for all v,w∈Av,w\in Av,w∈A and all λ∈F\lambda \in \mathbf{F}λ∈F.
TODO