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

Lemma multipar_Pi_B_proj: ∀ (G : context) D rho (A B A' B' : tm),
multipar G D (a_Pi rho A B) (a_Pi rho A' B')
→ (exists L, forall x, x `notin` L -> multipar G D (open_tm_wrt_tm B (a_Var_f x)) (open_tm_wrt_tm B' (a_Var_f x))).