Closes #97 🐔️👍

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Approved-by: loutr <l.ta-ma@proton.me>

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* chore: move the toplevel screenshot to the manual, as a listing

* feat(std): add `add` function over natural numbers, used as an example

* chore(docs): separate header style file for TeX + formatting

* Apply 4 suggestion(s) to 2 file(s)

* chore: update Cargo lock

* chore: update Proost version number

* docs: update manual

* docs: update specifications

* feat: mentionn GitHub mirror in README and update logo link

* docs(parser): incorrect documentation for commands

* docs(kernel: axiom, trace): fix documentation and try to make it more uniform

* docs(elaboration): fix links and typos in documentation