reserve fi,psi for Ordinal-Sequence,
  A,A1,B,C,D for Ordinal,
  X,Y for set,
  x,y for object;

theorem Th44:
  {} <> dom fi & C <> {} & sup fi is limit_ordinal implies sup (fi
  *^C) = (sup fi)*^C
proof
A1: for A,B st A in dom fi & B = fi.A holds (fi*^C).A = B*^C by Def4;
  dom (fi*^C) = dom fi by Def4;
  hence thesis by A1,Th42;
end;
