reserve r,r1,r2, s,x for Real,
  i for Integer;

theorem
  PI/2+2*PI*i <= r & r <= 3/2*PI+2*PI*i implies cos r <= 0
proof
  assume PI/2+2*PI*i <= r & r <= 3/2*PI+2*PI*i;
  then
  PI/2+2*PI*i < r & r < 3/2*PI+2*PI*i or PI/2+2*PI*i = r or r = 3/2*PI+2*
  PI*i by XXREAL_0:1;
  hence thesis by Th14,COMPLEX2:9,SIN_COS:77;
end;
