
theorem
  for V being non empty RLSStruct, M,N being Affine Subset of V holds M
  /\ N is Affine
proof
  let V be non empty RLSStruct;
  let M,N be Affine Subset of V;
  for x,y being VECTOR of V, a being Real
    st x in M /\ N & y in M /\ N
  holds (1 - a) * x + a * y in M /\ N
  proof
    let x,y be VECTOR of V;
    let a be Real;
    assume
A1: x in M /\ N & y in M /\ N;
    then x in N & y in N by XBOOLE_0:def 4;
    then
A2: (1 - a) * x + a * y in N by Def4;
    x in M & y in M by A1,XBOOLE_0:def 4;
    then (1 - a) * x + a * y in M by Def4;
    hence thesis by A2,XBOOLE_0:def 4;
  end;
  hence thesis;
end;
