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 be
  Nat st i in dom f holds (f+*(i,d))/.i = d
proof
  let D be non empty set, f be FinSequence of D, d be Element of D, i be
  Nat;
  assume
A1: i in dom f;
  then i in dom(f+*(i,d)) by Th29;
  hence (f+*(i,d))/.i = (f+*(i,d)).i by PARTFUN1:def 6
    .= d by A1,Th30;
end;
