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;

theorem Th7:
  (for x st x in B holds g.x = f.x) implies f +* g|B = f
proof
  assume x in B implies g.x = f.x;
  then g|B = f|B by Th2;
  hence thesis by Th5,RELAT_1:59;
end;
