They are two sides of the same coin. "The right to circulation" tells people "you can go wherever you want", and tells States "you can't demand a travel permit every time someone wants to move". "The right to live" tells people "you may go on living if you want" but also "you can't stop people from living if they don't consent to it". The freedom to do something restricts another person's ability to stop you from doing that.
Yes, this is correct.
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