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 (dilation(C)).A c= (dilation(C)).B
  proof
    assume
    A1: A c= B;
    A2: (dilation(C)).A = C+A by Def2;
    (dilation(C)).B = C+B by Def2;
    hence thesis by A2,A1,Th16;
  end;
