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

theorem Th33:
  PI/2 < r & r <= 2*PI implies sin r < 1
proof
  assume
A1: PI/2 < r & r <= 2*PI & sin r >= 1;
  sin r <= 1 by Th4;
  hence thesis by A1,Th28,XXREAL_0:1;
end;
