  Now if you look at the proof net built from the derivations of \(\vdash \Gamma , (A_1\lpar A_2), \ldots ,(A_{n-1}\lpar A_n)\) obtained from \(\vdash \Gamma , A_1, A_2 , \ldots ,A_n\), you will see that all trace of the order of application of the rules has disappeared. In a sense, the proof nets are an equivalence class of sequent calculus derivations with respect to the derivation order of rules whose application commute.