reserve x for Real;

theorem Th20:
  sin|].PI/2,3/2*PI.[ is decreasing
proof
A1: for x st x in ].PI/2,3/2*PI.[ holds diff(sin,x) < 0
  proof
    let x;
    assume x in ].PI/2,3/2*PI.[;
    then 0 > cos.x by Th13;
    hence thesis by SIN_COS:68;
  end;
  ].PI/2,3/2*PI.[ is open by RCOMP_1:7;
  hence thesis by A1,FDIFF_1:26,ROLLE:10,SIN_COS:24,68;
end;
