reserve a,x,y for object, A,B for set,
  l,m,n for Nat;
reserve X,Y for set, x for object,
  p,q for Function-yielding FinSequence,
  f,g,h for Function;
reserve m,n,k for Nat, R for Relation;

theorem
  for f be Function, x be set st x in dom f holds f +* (x .--> f.x) = f
proof
  let f be Function;
  let x be set;
  assume x in dom f;
  hence f +* (x .--> f.x) = f +*(x,f.x) by Def2
    .= f by Th34;
end;
