reserve k,n,m for Nat,
  A,B,C for Ordinal,
  X for set,
  x,y,z for object;
reserve f,g,h,fx for Function,
  K,M,N for Cardinal,
  phi,psi for
  Ordinal-Sequence;

theorem Th12:
  (phi^psi)|(dom phi) = phi
proof
  dom (phi^psi) = (dom phi)+^(dom psi) by ORDINAL4:def 1;
  then dom phi c= dom (phi^psi) by ORDINAL3:24;
  then
A1: dom phi = (dom (phi^psi))/\(dom phi) by XBOOLE_1:28;
  for x being object st x in dom phi holds phi.x = (phi^psi).x
by ORDINAL4:def 1;
  hence thesis by A1,FUNCT_1:46;
end;
