How does one 'prove' that other than by appealing to a list of 'human rights', upon which you and the other commenter surely disagree? There is no fundamental philosophical principle beneath human rights in which it will rigorously generate a list of rights. It's a null question, and I suspect you know that.

The stellman of 'housing is a human right' is 'everyone should have adequate shelter', and that's a far more productive starting point. The 'right' angle adds nothing.