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

  rr for set,

  rseq for Real_Sequence;

theorem Th50:
  arcsec2 | [.-sqrt 2,-1.] = (sec | [.3/4*PI,PI.])"
proof
  set h = sec | ].PI/2,PI.];
A1: [.3/4*PI,PI.] c= ].PI/2,PI.] by Lm6,XXREAL_2:def 12;
  then (sec | [.3/4*PI,PI.])" = (h | [.3/4*PI,PI.])" by RELAT_1:74
    .= h" | (h.:[.3/4*PI,PI.]) by RFUNCT_2:17
    .= h" | rng (h | [.3/4*PI,PI.]) by RELAT_1:115
    .= h" | ([.-sqrt 2,-1.]) by A1,Th42,RELAT_1:74;
  hence thesis;
end;
