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

theorem Th32:
  3/2*PI < r & r <= 2*PI implies sin r > -1
proof
  assume
A1: 3/2*PI < r & r <= 2*PI & sin r <= -1;
  sin r >= -1 by Th3;
  hence thesis by A1,Th27,XXREAL_0:1;
end;
