XSLT check if one of sibling elements contain certain parameter

I have XML which lists my menu items. Problem is, it lists all items regardless of their language and I need to filter out all items that don't belong to current language which is stored in $language variable.

This is my XSLT which is supposed to filter out menu items that don't belong to current language (it's also supposed to filter hidden items):

<xsl:apply-templates select="page[not(types/type = 'hidden' or types/type != $language)]"/>

Currently, only about element get's through and that is probably because my Home item also has index besides en.

So, how can I filter out element if it doesn't contain correct type with current language in it, while ignoring other properties?

This is my XML:

<navigation>
    <page handle="en" id="1">
        <name>Home</name>
        <types>
            <type>en</type>
            <type>index</type>
        </types>
    </page>
    <page handle="he" id="2">
        <name>Home HE</name>
        <types>
            <type>he</type>
        </types>
    </page>
    <page handle="about" id="3">
        <name>About</name>
        <types>
            <type>en</type>
        </types>
    </page>
</navigation>