Theme_Upgrader::check_package

			// Prevent credentials auth screen from displaying multiple times.
			if ( false === $result ) {
				break;
			}
		} // End foreach $themes.

		$this->maintenance_mode( false );

		// Refresh the Theme Update information.
		wp_clean_themes_cache( $parsed_args['clear_update_cache'] );

		/** This action is documented in wp-admin/includes/class-wp-upgrader.php */
		do_action(
			'upgrader_process_complete',
			$this,
			array(
				'action' => 'update',
				'type'   => 'theme',
				'bulk'   => true,
				'themes' => $themes,
			)
		);

		$this->skin->bulk_footer();

		$this->skin->footer();

		// Cleanup our hooks, in case something else does a upgrade on this connection.
		remove_filter( 'upgrader_pre_install', array( $this, 'current_before' ) );
		remove_filter( 'upgrader_post_install', array( $this, 'current_after' ) );
		remove_filter( 'upgrader_clear_destination', array( $this, 'delete_old_theme' ) );

		// Ensure any future auto-update failures trigger a failure email by removing
		// the last failure notification from the list when themes update successfully.
		$past_failure_emails = get_option( 'auto_plugin_theme_update_emails', array() );

		foreach ( $results as $theme => $result ) {
			// Maintain last failure notification when themes failed to update manually.
			if ( ! $result || is_wp_error( $result ) || ! isset( $past_failure_emails[ $theme ] ) ) {
				continue;
			}

			unset( $past_failure_emails[ $theme ] );
		}

		update_option( 'auto_plugin_theme_update_emails', $past_failure_emails );

		return $results;
	}

	/**
	 * Check that the package source contains a valid theme.
	 *
	 * Hooked to the {@see 'upgrader_source_selection'} filter by Theme_Upgrader::install().
	 * It will return an error if the theme doesn't have style.css or index.php
	 * files.
	 *
	 * @since 3.3.0
	 *
	 * @global WP_Filesystem_Base $wp_filesystem WordPress filesystem subclass.