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

theorem Th43:
  {} <> dom fi implies sup (C+^fi) = C+^sup fi
proof
A1: for A,B st A in dom fi & B = fi.A holds (C+^fi).A = C+^B by Def1;
  dom (C+^fi) = dom fi by Def1;
  hence thesis by A1,Th39;
end;
