reserve A for set,
  C for non empty set,
  B for Subset of A,
  x for Element of A,
  f,g for Function of A,C;
reserve B for Element of Fin A;

theorem Th10:
  (for x st x in B holds g.x = f.x) implies f +* g|B = f
proof
  reconsider C = B as Subset of A by FINSUB_1:16;
  (for x st x in C holds g.x = f.x) implies f +* g|C = f by Th7;
  hence thesis;
end;
