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

theorem Th35:
  0 <= r & r < PI implies cos r > -1
proof
  assume that
A1: 0 <= r and
A2: r < PI;
A3: cos r >= -1 by Th5;
  r <= 2*PI by A2,Lm10,XXREAL_0:2;
  hence thesis by A1,A2,A3,Th29,XXREAL_0:1;
end;
