
theorem
  for X being non empty set, Y being non empty Subset of ExtREAL, F
being Function of X,Y, x being Element of X st Y c= REAL holds -infty <F.x & F.
  x <+infty
proof
  let X be non empty set, Y be non empty Subset of ExtREAL, F be Function of X
  ,Y, x be Element of X;
A1: -infty <= F.x by XXREAL_0:5;
  assume Y c= REAL;
  hence thesis by A1,XXREAL_0:1,4;
end;
