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

  rr for set,

  rseq for Real_Sequence;

theorem Th75:
  arccosec1.(-1) = -PI/2 & arccosec1.(-sqrt 2) = -PI/4
proof
A1: arccosec1.(-1) = arccosec1 (-1) .= -PI/2 by Th32,Th71;
A2: -PI/2 <= -PI/4 by Lm7,XXREAL_1:3;
  arccosec1.(-sqrt 2) = arccosec1 (-sqrt 2) .= -PI/4 by A2,Th32,Th71;
  hence thesis by A1;
end;
