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

Lemma multipar_CPi_B_proj:  ∀ (G : context) D (A B a A' B' a' T T': tm),
multipar G D (a_CPi (Eq A B T) a) (a_CPi (Eq A' B' T') a')
→ (exists L, forall c, c `notin` L -> multipar G D (open_tm_wrt_co a (g_Var_f c)) (open_tm_wrt_co a' (g_Var_f c))).