theorem Th65:
  for F being Function st [:{a},rng p:] c= dom F & r = F[;](a,p)
  holds len r = len p
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 3;
end;
