Given the diagonal lema stated as above:
Diagonal Lema. Let $\mathfrak{T}$ be a theory wich is capable of representing the primitive recursive functions, and a codification schema for formulas in $\mathfrak{T}$ such that $\ulcorner \phi \urcorner$ is the codification of $\phi$. For all formulas $\psi(x)$ where $x$ is it's only free variable, we have $\mathfrak{T} \vdash \delta \leftrightarrow \psi(\ulcorner \delta \urcorner)$.
Why is it called after Cantor's diagonal arugment? Giving the justification why the standard diagonalization technique for demonstrating that the set of reals isn't countable is straightforward, but for this lemma it isn't.