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

  rr for set,

  rseq for Real_Sequence;

theorem Th82:
  arcsec2|[.-sqrt 2,-1.] is increasing
proof
  [.-sqrt 2,-1.] = sec.:[.3/4*PI,PI.] & [.3/4*PI,PI.] c= ].PI/2,PI.] by Lm6
,Th42,RELAT_1:115,XXREAL_2:def 12;
  hence thesis by Th78,RELAT_1:123,RFUNCT_2:28;
end;
