User:IssaRice/Computability and logic/S–m–n theorem

The s–m–n theorem states that if ${\phi }_e$ is an $(m+n)$ place computable partial function and $a_1,\dots ,a_m$ are natural numbers, then there exists a primitive recursive function $s_n^m$ such that ${\phi }_{s_n^m(e,a_1,\dots ,a_m)}\simeq \lambda y_1\cdots y_n[{\phi }_e(x_1,\dots ,x_m,y_1,\dots ,y_n)]$.