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;
reserve A,B,I for set, X,Y for ManySortedSet of I;

theorem
 I c= A \/ B & X|B = Y|B implies X,Y equal_outside A
proof
  dom X = I & dom Y = I by PARTFUN1:def 2;
 hence thesis by Th133;
end;
