reserve a,x,y for object, A,B for set,
  l,m,n for Nat;

theorem
  for D be non empty set, f be FinSequence of D, d,e be Element of D, i
  be Nat holds f+*(i,f/.i) = f
proof
  let D be non empty set, f be FinSequence of D, d,e be Element of D, i be
  Nat;
  per cases;
  suppose
    i in dom f;
    hence f+*(i,f/.i) = f+*(i,f.i) by PARTFUN1:def 6
      .= f by Th34;
  end;
  suppose
    not i in dom f;
    hence thesis by Def2;
  end;
end;
