reserve x,x0, r,r1,r2 for Real,
      th for Real,

  rr for set,

  rseq for Real_Sequence;

theorem Th70:
  PI/2 < r & r <= PI implies arcsec2 sec.r = r
proof
A1: dom (sec | ].PI/2,PI.]) = ].PI/2,PI.] by Th2,RELAT_1:62;
  assume PI/2 < r & r <= PI;
  then
A2: r in ].PI/2,PI.];
  then arcsec2 sec.r = arcsec2.((sec|].PI/2,PI.]).r) by FUNCT_1:49
    .= (id ].PI/2,PI.]).r by A2,A1,Th66,FUNCT_1:13
    .= r by A2,FUNCT_1:18;
  hence thesis;
end;
