reserve p,q,r,th,th1 for Real;
reserve n for Nat;

theorem
  sin|].0,PI/2.[ is increasing
proof
  for th st th in ].0,PI/2.[ holds 0 < diff(sin,th)
  proof
    let th;
    assume th in ].0,PI/2.[;
    then cos.th > 0 by SIN_COS:80;
    hence thesis by SIN_COS:68;
  end;
  hence thesis by FDIFF_1:26,ROLLE:9,SIN_COS:24,68;
end;
