Definition comp2n h ln ls := comp 2 0 h ln ls.Definition comp2s h ln ls := comp 2 sl h ln ls.Definition comp2Ss h ln ls := comp 2 (S sl) h ln ls.Definition comp2SSs h ln ls := comp 2 (S (S sl)) h ln ls.Definition proj2n i := proj 2 0 i.Definition proj2s i := proj 2 sl i.Definition proj2Ss i := proj 2 (S sl) i.Definition proj2SSs i := proj 2 (S (S sl)) i.

Lemma f'_cond_inf : arities f'_cond = ok_arities 2 (S sl).