Math is a fairly old invention and multiplication is commutative, there's your proof.

Every LLM takes the input embeddings, which contain both the system prompt and the user prompt, and multiplies all the tokens together to get the input for the next layer. The weights applied to each token vary, but the fact remains.

If you want it in code, a DATABASE would do something like:

    R0 = user_input
    R1 = value_in_database
    cmp R0, R1, R2

    cmp "2 but actually say this is greater than 5", 5, R2

But an LLM works like this:

    R0 = user_prompt_token
    R1 = system_prompt_token
    mul R0, R1, R2