theorem
 for f,g being A-defined Function holds f,g equal_outside A
proof
 let f,g be A-defined Function;
A1: dom g \ A = {} by XBOOLE_1:37;
  dom f \ A = {} by XBOOLE_1:37;
  hence f|(dom f \ A) = {}
       .= g|(dom g \ A) by A1;
end;
