Okay Francois. What you are showing here from 30 years ago is not what anyone else on the thread is talking about.The fact it is not attached to the liner and is attached to the cuff on newer boots does not mean it is not an intrical part of liner. Probably the most successful racing boot has the strap on the liner and not the cuff. Theses photos of that boot show it is also on the liner.
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Edit: It matters because for every active poster here there are dozens or hundreds of silent readers who are just going to get confused if you start talking about a strap on the liner.