(* Advanced inversion lemmas on context-sensitive reducible terms ***********)
(* Note: this property is unusual *)
-lemma cnx_inv_crx: ∀h,g,L,T. ⦃G, L⦄ ⊢ 𝐑[h, g]⦃T⦄ → ⦃G, L⦄ ⊢ 𝐍[h, g]⦃T⦄ → ⊥.
-#h #g #L #T #H elim H -L -T
+lemma cnx_inv_crx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ 𝐑[h, g]⦃T⦄ → ⦃G, L⦄ ⊢ 𝐍[h, g]⦃T⦄ → ⊥.
+#h #g #G #L #T #H elim H -L -T
[ #L #k #l #Hkl #H
lapply (cnx_inv_sort … H) -H #H
- lapply (deg_mono … H Hkl) -h -L -k <plus_n_Sm #H destruct
+ lapply (deg_mono … H Hkl) -h -L -k <plus_n_Sm #H destruct
| #I #L #K #V #i #HLK #H
elim (cnx_inv_delta … HLK H)
| #L #V #T #_ #IHV #H