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

  rr for set,

  rseq for Real_Sequence;

theorem Th76:
  arccosec2.(sqrt 2) = PI/4 & arccosec2.1 = PI/2
proof
A1: arccosec2.1 = arccosec2 1 .= PI/2 by Th32,Th72;
A2: PI/4 <= PI/2 by Lm8,XXREAL_1:2;
  arccosec2.(sqrt 2) = arccosec2 (sqrt 2) .= PI/4 by A2,Th32,Th72;
  hence thesis by A1;
end;
