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Oh well, back to the drawing board.
Either test for a URL ending in "/" to know that it is for an index page... or you can test for SCRIPT_NAME or somesuch which will tell you the name of the file on the server that the requested URL was mapped to. In this case, even though the requested URL was "/", SCRIPT_NAME will return "/index.html" for you.
Whatever you do, the URL used out on the web (i.e. in links), should be the one ending in a slash, and not including the index file filename itself.