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

theorem
  cos|].0,PI/2.[ is decreasing
proof
  for th st th in ].0,PI/2.[ holds diff(cos,th) < 0
  proof
    let th;
    assume th in ].0,PI/2.[;
    then 0 < sin.(th) by Lm1;
    then diff(cos,th) = -sin.(th) & 0-sin.(th) < 0 by SIN_COS:67;
    hence thesis;
  end;
  hence thesis by FDIFF_1:26,ROLLE:10,SIN_COS:24,67;
end;
