reserve x,y for object,
        D,D1,D2 for non empty set,
        i,j,k,m,n for Nat,
        f,g for FinSequence of D*,
        f1 for FinSequence of D1*,
        f2 for FinSequence of D2*;
reserve f for complex-valued Function,
        g,h for complex-valued FinSequence;

theorem
   for f be FinSequence
     for o1,o2 be valued_reorganization of f st
       rng (f*.o1.i) = rng (f*.o2.i)
   holds
     rng (o1.i) = rng (o2.i) by Lm7;
