+
+(* Inversion lemmas with advanced rt_computation for terms ******************)
+
+lemma nta_inv_abst_bi_cnv (a) (h) (p) (G) (K) (W):
+ ∀T,U. ⦃G,K⦄ ⊢ ⓛ{p}W.T :[a,h] ⓛ{p}W.U →
+ ∧∧ ⦃G,K⦄ ⊢ W ![a,h] & ⦃G,K.ⓛW⦄ ⊢ T :[a,h] U.
+#a #h #p #G #K #W #T #U #H
+elim (cnv_inv_cast … H) -H #X #HWU #HWT #HUX #HTX
+elim (cnv_inv_bind … HWU) -HWU #HW #HU
+elim (cnv_inv_bind … HWT) -HWT #_ #HT
+elim (cpms_inv_abst_sn … HUX) -HUX #W0 #X0 #_ #HUX0 #H destruct
+elim (cpms_inv_abst_bi … HTX) -HTX #_ #HTX0 -W0
+/3 width=3 by cnv_cast, conj/
+qed-.