(* ------------------------------------------------------------- *)

Lemma multipar_Pi_exists: ∀ x (G : context) D rho (A B A' B' : tm),
lc_tm (a_Pi rho A B) -> x `notin` fv_tm_tm_tm B -> multipar G D A A'
→ multipar G D (open_tm_wrt_tm B (a_Var_f x)) B'
→ multipar G D (a_Pi rho A B) (a_Pi rho A' (close_tm_wrt_tm x B')).