reserve P,Q,X,Y,Z for set, p,x,x9,x1,x2,y,z for object;
reserve D for non empty set;

theorem Th81:
  for f being PartFunc of X,Y for g being set st g in TotFuncs(f)
  holds g is Function of X,Y
proof
  let f be PartFunc of X,Y;
  let g be set;
  assume g in TotFuncs(f);
  then
  ex g9 being PartFunc of X,Y st g9 = g & g9 is total & f tolerates g9 by
PARTFUN1:def 5;
  hence thesis;
end;
