reserve x for Real;

theorem Th22:
  cos|].PI,2*PI.[ is increasing
proof
A1: for x st x in ].PI,2*PI.[ holds diff(cos,x) > 0
  proof
    let x;
    assume x in ].PI,2*PI.[;
    then 0-sin.x > 0 by Th9,XREAL_1:50;
    hence thesis by SIN_COS:67;
  end;
  ].PI,2*PI.[ is open by RCOMP_1:7;
  hence thesis by A1,FDIFF_1:26,ROLLE:9,SIN_COS:24,67;
end;
