What is the standard reference for the provability of the cut-elimination theorem in PRA?


Update: Rasmus Blanck has offered a reference for a system other than Gentzen's $\mathfrak L \mathfrak K$. The bounty is for a reference for the provability of the cut-elimination theorem for the sequent calculus $\mathfrak L \mathfrak K$ in PRA.



cut-elimination provable in PRA
My suggestion is Theorem 5.17 in section V.5.(d) of Hájek and Pudlák's *Metamathematics of First-Order Arithmetic*, Springer-Verlag, 1993. There, cut-elimination is shown to be provable in the even weaker theory $I\Delta\_0 + \text{superexp}$.


