reserve E for RealLinearSpace;
reserve A, B, C for binary-image of E;
reserve a, b, v for Element of E;
reserve F, G for binary-image-family of E;
reserve A, B, C for non empty binary-image of E;

theorem
  A c= B implies C(-)B c= C(-)A
  proof
    assume
    A1: A c= B;
    let x be object;
    assume x in C(-)B;
    then consider w be Element of E such that
    A2: x = w & for b be Element of E st b in B holds w - b in C;
    for a be Element of E st a in A holds w - a in C by A1,A2;
    hence x in C(-)A by A2;
  end;
