reserve i,j,n,k,m for Nat,
     a,b,x,y,z for object,
     F,G for FinSequence-yielding FinSequence,
     f,g,p,q for FinSequence,
     X,Y for set,
     D for non empty set;

theorem Th40:
  for f,g be with_evenly_repeated_values FinSequence holds
     f^g is with_evenly_repeated_values
proof
  let f,g be with_evenly_repeated_values FinSequence;
  set fg=f^g;
  let y be object;
  reconsider c1=card (f"{y}),c2=card (g"{y}) as even Nat by Def6;
  card (fg"{y}) = c1+c2 by FINSEQ_3:57;
  hence card (fg"{y}) is even;
end;
