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

theorem Th34:
  0 < r & r < 2*PI implies cos r < 1
proof
  assume 0 < r & r < 2*PI;
  then
A1: cos r <> 1 by COMPTRIG:61;
  cos r <= 1 by Th6;
  hence thesis by A1,XXREAL_0:1;
end;
