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

Lemma multipar_CPi_exists:  ∀ c (G : context) D (A B a T A' B' a' T': tm),
lc_tm (a_CPi (Eq A B T) a) -> c `notin` fv_co_co_tm a -> multipar G D A A'
→ multipar G D B B' -> multipar G D T T'
→ multipar G D (open_tm_wrt_co a (g_Var_f c)) a'
→ multipar G D (a_CPi (Eq A B T) a) (a_CPi (Eq A' B' T') (close_tm_wrt_co c a')).