theorem
  sin(a-b) = sin(a)*cos(b)-cos(a)*sin(b)
proof
  thus sin(a-b) =(sin.a) *(cos.(-b))+(cos.a) * (sin.(-b)) by Th73
    .=(sin.a) *(cos.b)+(cos.a) * (sin.(-b)) by Th30
    .=(sin.a) *(cos.b)+(cos.a) * -(sin.b) by Th30
    .=(sin a) *(cos b)-(cos a) * (sin b);
end;
