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

theorem
  -PI/2+2*PI*i <= r & r <= PI/2+2*PI*i implies cos r >= 0
proof
  assume -PI/2+2*PI*i <= r & r <= PI/2+2*PI*i;
  then
  -PI/2+2*PI*i < r & r < PI/2+2*PI*i or -PI/2+2*PI*i = r or r = PI/2+2*PI*
  i by XXREAL_0:1;
  hence thesis by Th9,Th13,COMPLEX2:9,SIN_COS:77;
end;
