feat: add Bitvec reverse definition, getLsbD_reverse, getMsbD_reverse, reverse_append, reverse_replicate and Nat.mod_sub_eq_sub_mod

[luisacicolini]

This PR defines reverse for bitvectors and implements a first subset of theorems (getLsbD_reverse, getMsbD_reverse, reverse_append, reverse_replicate) and an additional theorem necessary for one of the proofs (Nat.mod_sub_eq_sub_mod).

The main objective is to simplify the proofs in #6326. I sadly could not find a way to avoid adding Nat.mod_sub_eq_sub_mod, any suggestion in this direction would be greatly helpful.

[leanprover-community-bot]

Mathlib CI status (docs):

• ❗ Batteries/Mathlib CI will not be attempted unless your PR branches off the nightly-with-mathlib branch. Try git rebase 9b28c5879a77f9f0212a7f39ea83f56c71abda42 --onto 2c87905d77b707c3283c1de759fd63269ac386a1. (2024-12-31 15:59:57)

[alexkeizer]

Suggested change

	/-- Reverse of a Bitvec. We treat BitVec as lists of bools. -/
	/-- Reverse the bits in a bitvector. -/

We generally phrase a docstring for a function as an action/verb rather than just the result/noun.

I also wouldn't mention that we treat a bitvector as a list of bools, that's the "expected" interpretation of a bitvector (list of bools is more or less the same as a "vector of bits").

I guess you're referring here to the fact that the implementation is more in the style of a List.reverse versus other definitions that rely on the Nat-based internal encoding. That kind of comment feels more appropriate as a local comment rather than a docstring, but even then, I'm not sure it needs mentioning; it's clear from the code already.

[alexkeizer]

Suggested change

	def reverse : (w : Nat) → BitVec w → BitVec w
	def reverse : {w : Nat} → BitVec w → BitVec w

w can be inferred from the bitvector arg, and can thus be implicit

[alexkeizer]

I'm missing a msb_reverse specialization