feat: soundness and completeness of linear logic phase semantics

[tannerduve]

This PR proves that the sequent calculus for full classical linear logic (CLL) is sound with respect to phase semantics, and proves completeness for MALL, the multiplicative-additive fragment of classical linear logic. Specifically it shows that every provable sequent is valid in every phase space, and constructs a syntactic phase model to prove that semantic validity implies provability for MALL.

Note on AI usage: Aleph prover proved several lemmas used in proving completeness, and these proofs were heavily iterated on and golfed by me, ensuring they meet style standards.

A couple of proofs could possibly be further golfed, open to receiving help with this

[chenson2018]

Could you please do a pass fixing indentation issues? I started to mark them all individually but I think it is just easier to point out that this in general doesn't adhere to indentation at four spaces for theorem statements using multiple lines.

[tannerduve]

Could you please do a pass fixing indentation issues? I started to mark them all individually but I think it is just easier to point out that this in general doesn't adhere to indentation at four spaces for theorem statements using multiple lines.

definitely. I was unaware of this convention for some reason.

[tannerduve]

just fixed, lmk if there are other issues wrt indentation or style conventions I've missed

[chenson2018]

This isn't comprehensive, but a few style things I noticed. The formatting in general is a bit rough at the moment, I assume because of the AI usage.

I'd prefer to have @fmontesi review the actual content.