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, h being Function
  holds h+*f, h+*g equal_outside A
proof
 let f,g be A-defined Function, h be Function;
   h, h+*f equal_outside A by Th129;
   then
A1: h+*f,h equal_outside A;
   h, h+*g equal_outside A by Th129;
 hence thesis by A1;
end;
