reserve x for Real;

theorem Th19:
  sin|].-PI/2,PI/2.[ is increasing
proof
A1: for x st x in ].-PI/2,PI/2.[ holds diff(sin,x) > 0
  proof
    let x;
    assume x in ].-PI/2,PI/2.[;
    then 0 < cos.x by Th11;
    hence thesis by SIN_COS:68;
  end;
  ].-PI/2,PI/2.[ is open by RCOMP_1:7;
  hence thesis by A1,FDIFF_1:26,ROLLE:9,SIN_COS:24,68;
end;
