(* 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 #l #Hkl #H
+[ #L #k #d #Hkd #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 Hkd) -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
elim (cnx_inv_appl … H) -H /2 width=1 by/
| #I #L #V #T * #H1 #H2 destruct
[ elim (cnx_inv_zeta … H2)
- | elim (cnx_inv_tau … H2)
+ | elim (cnx_inv_eps … H2)
]
|6,7: #a * [ elim a ] #L #V #T * #H1 #_ #IH #H2 destruct
[1,3: elim (cnx_inv_abbr … H2) -H2 /2 width=1 by/