Multi-part form and wp_redirect()

You have a form like

<form action="http://some/url/form_two.php" method="POST">
 <input type="whatever" value="nothing" />
 <input type="hidden" name="form_one_displayed" value="1" />
 <input type="submit" value="Send" />
</form>

in e.g form_one.php

In form_two.php you validate the data that was send (or not)

<?php
$result = do_some_validation_with( $_POST );

if ( false == $result )
  wp_redirect( 'form_one.php' );
else
  display_form_two();

function do_some_validation_with( $postdata = array() ) {
  // nothing was send
  if ( empty( $postdata ) )
    return false;

  // if the first form wasn't send, stop validation
  if ( ! isset( $postdata['form_one_displayed'] ) )
    return false;

  // do more validation

  // if validation pass
  return true;
}

function display_form_two() {}

I think it is easier to use an ajax request to validate the form data and display the second form only if the first one was validated.