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 be Element of D, i,j
  be Nat st i <> j & j in dom f holds (f+*(i,d))/.j = f/.j
proof
  let D be non empty set, f be FinSequence of D, d be Element of D, i,j be
  Nat such that
A1: i <> j and
A2: j in dom f;
  j in dom(f+*(i,d)) by A2,Th29;
  hence (f+*(i,d))/.j = (f+*(i,d)).j by PARTFUN1:def 6
    .= f.j by A1,Th31
    .= f/.j by A2,PARTFUN1:def 6;
end;
