reserve a,x,y for object, A,B for set,
  l,m,n for Nat;
reserve X,Y for set, x for object,
  p,q for Function-yielding FinSequence,
  f,g,h for Function;
reserve m,n,k for Nat, R for Relation;
reserve i,j for Nat;
reserve F for Function,
  e,x,y,z for object;
reserve a,b,c for set;

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;
