+/3 width=1 by cpcs_cprs_sn, conj/
+qed-.
+
+lemma nta_inv_ldec_sn_cnv (h) (a) (G) (K) (V):
+ ∀X2. ❨G,K.ⓛV❩ ⊢ #0 :[h,a] X2 →
+ ∃∃U. ❨G,K❩ ⊢ V ![h,a] & ⇧[1] V ≘ U & ❨G,K.ⓛV❩ ⊢ U ⬌*[h] X2 & ❨G,K.ⓛV❩ ⊢ X2 ![h,a].
+#h #a #G #Y #X #X2 #H
+elim (cnv_inv_cast … H) -H #X1 #HX2 #H1 #HX21 #H2
+elim (cnv_inv_zero … H1) -H1 #Z #K #V #HV #H destruct
+elim (cpms_inv_ell_sn … H2) -H2 *
+[ #_ #H destruct
+| #m #W #HVW #HWX1 #H destruct
+ elim (lifts_total V (𝐔❨1❩)) #U #HVU
+ lapply (cpms_lifts_bi … HVW (Ⓣ) … (K.ⓛV) … HVU … HWX1) -W
+ [ /3 width=1 by drops_refl, drops_drop/ ] #HUX1
+ /3 width=5 by cprs_div, ex4_intro/
+]