
theorem Th21:
  for X,Y be non empty set, f be PartFunc of X,ExtREAL, r be Real
    st f = Y --> r holds f is without-infty without+infty
proof
    let X,Y be non empty set, f be PartFunc of X,ExtREAL, r be Real;
    assume A1: f = Y --> r; then
    for x be object holds f.x > -infty by XREAL_0:def 1,XXREAL_0:12;
    hence f is without-infty by MESFUNC5:def 5;
    for x be object holds f.x < +infty by A1,XREAL_0:def 1,XXREAL_0:9;
    hence f is without+infty by MESFUNC5:def 6;
end;
