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