reserve x for Real;

theorem Th21:
  cos|].0,PI.[ is decreasing
proof
A1: for x st x in ].0,PI.[ holds diff(cos,x) < 0
  proof
    let x;
    assume x in ].0,PI.[;
    then 0 < sin.x by Th7;
    then 0-sin.x < 0;
    hence thesis by SIN_COS:67;
  end;
  ].0,PI.[ is open by RCOMP_1:7;
  hence thesis by A1,FDIFF_1:26,ROLLE:10,SIN_COS:24,67;
end;
