theorem Th7:
  sin(r) = 0 implies ex i st r = PI*i
  proof
    assume sin(r) = 0;
    then r = 2*PI*[\r/(2*PI)/] or r = PI+2*PI*[\r/(2*PI)/] by Th5;
    then r = PI*(2*[\r/(2*PI)/]) or r = PI*(1+2*[\r/(2*PI)/]);
    hence thesis;
  end;
