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

theorem Th70:
  x <> +infty & x <> -infty & x * y = -infty implies y = +infty or y = -infty
proof
  assume that
A1: x <> +infty & x <> -infty and
A2: x * y = -infty;
  assume y <> +infty & y <> -infty;
  then
A3: y in REAL by XXREAL_0:14;
  x in REAL by A1,XXREAL_0:14;
  then reconsider a=x, b=y as Real by A3;
  x * y = a * b;
  hence contradiction by A2;
end;
