theorem
  -1 < r & r < 1 implies PI/4 < arccot r & arccot r < 3/4*PI
proof
  assume that
A1: -1 < r and
A2: r < 1;
A3: arccot r <= 3/4*PI by A1,A2,Th64;
  PI/4 <= arccot r by A1,A2,Th64;
  then
  PI/4 < arccot r & arccot r < 3/4*PI or PI/4 = arccot r or arccot r = 3/4
  *PI by A3,XXREAL_0:1;
  hence thesis by A1,A2,Th18,Th52;
end;
