reserve a,x,y for object, A,B for set,
  l,m,n for Nat;

theorem Th28:
  for f,g being Function, A be set st dom g c= A holds f, f +* g
  equal_outside A
proof
  let f,g be Function, A be set;
  assume
A1: dom g c= A;
A2: dom(f +* g) \ A = (dom f \/ dom g) \ A by FUNCT_4:def 1
    .= dom f \ A \/ (dom g \ A) by XBOOLE_1:42
    .= dom f \ A \/ {} by A1,XBOOLE_1:37
    .= dom f \ A;
  dom f \ A misses A by XBOOLE_1:79;
  then dom f \ A misses dom g by A1,XBOOLE_1:63;
  hence f|(dom f \ A) = (f +* g)|(dom(f +* g) \ A) by A2,FUNCT_4:72;
end;
