In this section, Kleene builds a formal system for primitive recursive functions. The beginning of the proof for lemma IId is skipped because it comes for general properties, but I must be missing something.

We easily see, by general properties of $\vdash$, that $E^{\psi_{1}...\psi_{l}}_{f_{1}...f_{l}},E_{l+1}...E_k\vdash f_i($x$_1,...,$x$_{n_{i}}) = $ x, if

$f_i($x$_1,...,$x$_{n_{i}}) = $ x $\in E^{\phi_i}_{f_{i}}$

What is the justification in this?

(Sorry, I couldn't put more background information this is lemma four of five lemmas. It would be too much to describe in one question, so just refer to the text. Thanks)


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.