Simulations of the arithmetic file

[clarus]

We focus on verifying the Paris version of the EVM. We will start with the arithmetic.py file that describes the primitive arithmetic operations. The relevant files are:

• the Python source file: https://github.com/ethereum/execution-specs/blob/master/src/ethereum/paris/vm/instructions/arithmetic.py
• the translated version in Coq: https://github.com/formal-land/coq-of-python/blob/main/CoqOfPython/ethereum/paris/vm/instructions/arithmetic.v (generated)
• the simulation (written by hand): https://github.com/formal-land/coq-of-python/blob/main/CoqOfPython/ethereum/paris/vm/instructions/simulations/arithmetic.v
• the proof of equivalence between the simulation and the translated code: https://github.com/formal-land/coq-of-python/blob/main/CoqOfPython/ethereum/paris/vm/instructions/proofs/arithmetic.v (not working yet)

The goal of this task is to complete the simulation file to have a definition for rest of the functions:

• add
• sub
• mul
• div
• sdiv
• mod
• smod
• addmod
• mulmod
• exp
• signextend

This might require adding some definitions for functions in other files as well, when they are called. For now, only the add function is defined.