theorem Th64:
  for F being Function st [:{a},rng p:] c= dom F holds F[;](a,p) is FinSequence
proof
  let F be Function;
  assume [:{a},rng p:] c= dom F;
  then dom(F[;](a,p)) = dom p by Lm4;
  then dom(F[;](a,p)) = Seg len p by FINSEQ_1:def 3;
  hence thesis by FINSEQ_1:def 2;
end;
