
theorem
  for V being vector-distributive scalar-distributive scalar-associative
  scalar-unital non empty RLSStruct, v being VECTOR
  of V holds {v} is Affine
proof
  let V be vector-distributive scalar-distributive scalar-associative
  scalar-unital non empty RLSStruct;
  let v be VECTOR of V;
  for x,y being VECTOR of V, a being Real
    st x in {v} & y in {v} holds (1-a)*x + a*y in {v}
  proof
    let x,y being VECTOR of V;
    let a be Real;
    assume x in {v} & y in {v};
    then x = v & y = v by TARSKI:def 1;
    then (1-a)*x + a*y = ((1-a)+a)*v by RLVECT_1:def 6
      .= v by RLVECT_1:def 8;
    hence thesis by TARSKI:def 1;
  end;
  hence thesis;
end;
