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

theorem Th27:
  for f,g be Function, A be set st f,g equal_outside A holds dom f
  \ A = dom g \ A
proof
  let f,g be Function, A be set;
  assume
A1: f|(dom f \ A) = g|(dom g \ A);
  thus dom f \ A = dom f /\ (dom f \ A) by XBOOLE_1:28
    .= dom(f|(dom f \ A)) by RELAT_1:61
    .= dom g /\ (dom g \ A) by A1,RELAT_1:61
    .= dom g \ A by XBOOLE_1:28;
end;
