Variable h0 h1 : BC.
Hypothesis h0_inf : arities h0 = ok_arities 1 (S sl).
Hypothesis h1_inf : arities h1 = ok_arities 1 (S sl).
Definition f'_then :=
comp2Ss h1 [proj2n 1]
([comp2Ss Y_e [proj2n 0; proj2n 1] [proj2Ss 3];
proj2Ss 2 ] ++ (map (proj 2 (S sl)) (seq 4 (sl - 1)))).
Transparent P_e Y_e.

Lemma f'_then_inf : arities f'_then = ok_arities 2 (S sl).
Opaque f'_then.