
theorem Th5:
for D be set, Y be FinSequenceSet of D, F be FinSequence of Y,
    k1,k2 be Nat st k1 <= k2
 holds Sum Length(F|k1) <= Sum Length(F|k2)
proof
   let D be set, Y be FinSequenceSet of D, F be FinSequence of Y, k1,k2 be Nat;
   assume k1 <= k2; then
   F|k2|k1 = F|k1 by FINSEQ_1:82; then
   F|k2 = (F|k1)^((F|k2)/^k1) by RFINSEQ8; then
   Length(F|k2) = Length(F|k1) ^ Length((F|k2)/^k1) by Th4; then
   Sum Length(F|k2) = Sum Length(F|k1) + Sum Length((F|k2)/^k1) by RVSUM_1:75;
   hence thesis by NAT_1:11;
end;
