reserve x,x1,x2,y,y9,y1,y2,z,z1,z2 for object,P,X,X1,X2,Y,Y1,Y2,V,Z for set;

theorem Th69:
  for f being PartFunc of X,Y for g being set st g in TotFuncs(f)
  holds g is PartFunc 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 Def5;
  hence thesis;
end;
