(* Main properties with generic candidates of reducibility ******************)
-theorem csx_gcr: ∀h,o. gcr (cpx h) (tdeq h o) (csx h o) (csx h o).
-#h #o @mk_gcr //
-[ /3 width=1 by csx_applv_cnx/
-|2,3,6: /2 width=1 by csx_applv_beta, csx_applv_sort, csx_applv_cast/
+theorem csx_gcr: ∀h. gcr (cpx h) tdeq (csx h) (csx h).
+#h @mk_gcr
+[ //
+| #G #L #Vs #Hvs #T #HT #H
+ @(csx_applv_cnx … H) -H // (**) (* auto fails *)
+| /2 width=1 by csx_applv_beta/
| /2 width=7 by csx_applv_delta/
-| #G #L #V1b #V2b #HV12b #a #V #T #H #HV
- @(csx_applv_theta … HV12b) -HV12b
- @csx_abbr //
+| /3 width=3 by csx_applv_theta, csx_abbr/
+| /2 width=1 by csx_applv_cast/
]
qed.