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

  rr for set,

  rseq for Real_Sequence;

theorem Th74:
  arcsec2.(-sqrt 2) = 3/4*PI & arcsec2.(-1) = PI
proof
A1: PI/2 < PI by Lm6,XXREAL_1:2;
A2: arcsec2.(-1) = arcsec2 (-1) .= PI by A1,Th31,Th70;
A3: PI/2 < 3/4*PI & 3/4*PI <= PI by Lm6,XXREAL_1:2;
  arcsec2.(-sqrt 2) = arcsec2 (-sqrt 2) .= 3/4*PI by A3,Th31,Th70;
  hence thesis by A2;
end;
