--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2/substitution/llpx_sn_ldrop.ma".
+include "basic_2/static/ssta.ma".
+
+(* STRATIFIED STATIC TYPE ASSIGNMENT FOR TERMS ******************************)
+
+(* Properties on lazy sn pointwise extensions *******************************)
+
+lemma ssta_llpx_sn_conf: ∀R. (∀I,L.reflexive … (R I L)) →
+ (∀I.l_liftable (R I)) →
+ ∀h,g,G. s_r_confluent1 … (ssta h g G) (llpx_sn R 0).
+#R #H1R #H2R #h #g #G #Ls #T1 #T2 #H elim H -G -Ls -T1 -T2
+[ /3 width=4 by llpx_sn_fwd_length, llpx_sn_sort/
+| #G #Ls #Ks #V1s #W2s #V2s #i #HLKs #_ #HVW2s #IHV12s #Ld #H elim (llpx_sn_inv_lref_ge_sn … H … HLKs) // -H
+ #Kd #V1d #HLKd #HV1s #HV1sd
+ lapply (ldrop_fwd_drop2 … HLKs) -HLKs #HLKs
+ lapply (ldrop_fwd_drop2 … HLKd) -HLKd #HLKd
+ @(llpx_sn_lift_le … HLKs HLKd … HVW2s) -HLKs -HLKd -HVW2s /2 width=1 by/ (**) (* full auto too slow *)
+| #G #Ls #Ks #V1s #W1s #l #i #HLKs #Hl #HVW1s #Ld #H elim (llpx_sn_inv_lref_ge_sn … H … HLKs) // -H
+ #Kd #V1d #HLKd #HV1s #HV1sd
+ lapply (ldrop_fwd_drop2 … HLKs) -HLKs #HLKs
+ lapply (ldrop_fwd_drop2 … HLKd) -HLKd #HLKd
+ @(llpx_sn_lift_le … HLKs HLKd … HVW1s) -HLKs -HLKd -HVW1s /2 width=1 by/ (**) (* full auto too slow *)
+| #a #I #G #Ls #V #T1 #T2 #_ #IHT12 #Ld #H elim (llpx_sn_inv_bind_O … H) -H
+ /4 width=5 by llpx_sn_bind_repl_SO, llpx_sn_bind/
+| #G #Ls #V #T1 #T2 #_ #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
+ /3 width=1 by llpx_sn_flat/
+| #G #Ls #V #T1 #T2 #_ #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
+ /3 width=1 by llpx_sn_flat/
+]
+qed-.