reserve x,y,z,w for ExtReal,
  r for Real;
reserve f,g for ExtReal;
reserve t for ExtReal;

theorem Th82:
  y" = 0 implies y = +infty or y = -infty or y = 0
proof
  assume
A1: y" = 0;
  assume y <> +infty & y <> -infty;
  then y in REAL by XXREAL_0:14;
  then reconsider y as Real;
  y"" = 0 by A1;
  hence thesis;
end;
