From 8b1bc0a74dbc6c5854cbce31240ae829dfe7e8bf Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Fri, 28 Sep 2012 20:45:20 +0000
Subject: [PATCH] - partial commit (static component only) - results on the
 transitive closure of ltpss

---
 .../lambda_delta/basic_2/grammar/lenv_px.ma   |  2 +-
 .../static/{aaa_ltpss.ma => aaa_ltpss_dx.ma}  | 32 ++++++-----
 .../aaa_ltpsss.etc => static/aaa_ltpss_sn.ma} | 23 ++++----
 .../{ssta_ltpss.ma => ssta_ltpss_dx.ma}       | 57 ++++++++++---------
 .../basic_2/static/ssta_ltpss_sn.ma           | 53 +++++++++++++++++
 5 files changed, 113 insertions(+), 54 deletions(-)
 rename matita/matita/contribs/lambda_delta/basic_2/static/{aaa_ltpss.ma => aaa_ltpss_dx.ma} (68%)
 rename matita/matita/contribs/lambda_delta/basic_2/{etc/ltpsss/aaa_ltpsss.etc => static/aaa_ltpss_sn.ma} (59%)
 rename matita/matita/contribs/lambda_delta/basic_2/static/{ssta_ltpss.ma => ssta_ltpss_dx.ma} (69%)
 create mode 100644 matita/matita/contribs/lambda_delta/basic_2/static/ssta_ltpss_sn.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/grammar/lenv_px.ma b/matita/matita/contribs/lambda_delta/basic_2/grammar/lenv_px.ma
index 9de1599e4..c3d05949f 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/grammar/lenv_px.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/grammar/lenv_px.ma
@@ -131,7 +131,7 @@ qed.
 
 lemma lpx_inv_TC: ∀R. reflexive ? R →
                   ∀L1,L2. lpx (TC … R) L1 L2 → TC … (lpx R) L1 L2.
-#R #HR #L1 #L2 #H elim H -L1 -L2 /2 width=1/ /3 width=3/
+#R #HR #L1 #L2 #H elim H -L1 -L2 /3 width=1/ /3 width=3/
 qed.
 
 lemma lpx_append: ∀R,K1,K2. lpx R K1 K2 → ∀L1,L2. lpx R L1 L2 →
diff --git a/matita/matita/contribs/lambda_delta/basic_2/static/aaa_ltpss.ma b/matita/matita/contribs/lambda_delta/basic_2/static/aaa_ltpss_dx.ma
similarity index 68%
rename from matita/matita/contribs/lambda_delta/basic_2/static/aaa_ltpss.ma
rename to matita/matita/contribs/lambda_delta/basic_2/static/aaa_ltpss_dx.ma
index c672f02fa..2f2d07360 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/static/aaa_ltpss.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/static/aaa_ltpss_dx.ma
@@ -13,16 +13,17 @@
 (**************************************************************************)
 
 include "basic_2/unfold/tpss_tpss.ma".
-include "basic_2/unfold/ltpss_ldrop.ma".
+include "basic_2/unfold/ltpss_dx_ldrop.ma".
 include "basic_2/static/aaa_lift.ma".
 
 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
 
-(* Properties about parallel unfold *****************************************)
+(* Properties about dx parallel unfold **************************************)
 
 (* Note: lemma 500 *)
-lemma aaa_ltpss_tpss_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2,d,e. L1 ▶* [d, e] L2 →
-                           ∀T2. L2 ⊢ T1 ▶* [d, e] T2 → L2 ⊢ T2 ⁝ A.
+lemma aaa_ltpss_dx_tpss_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A →
+                              ∀L2,d,e. L1 ▶* [d, e] L2 →
+                              ∀T2. L2 ⊢ T1 ▶* [d, e] T2 → L2 ⊢ T2 ⁝ A.
 #L1 #T1 #A #H elim H -L1 -T1 -A
 [ #L1 #k #L2 #d #e #_ #T2 #H
   >(tpss_inv_sort1 … H) -H //
@@ -30,21 +31,21 @@ lemma aaa_ltpss_tpss_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2,d,e. L1 ▶* [d
   elim (tpss_inv_lref1 … H) -H
   [ #H destruct
     elim (lt_or_ge i d) #Hdi
-    [ elim (ltpss_ldrop_conf_le … HL12 … HLK1 ?) -L1 /2 width=2/ #X #H #HLK2
-      elim (ltpss_inv_tpss11 … H ?) -H /2 width=1/ -Hdi #K2 #V2 #HK12 #HV12 #H destruct
+    [ elim (ltpss_dx_ldrop_conf_le … HL12 … HLK1 ?) -L1 /2 width=2/ #X #H #HLK2
+      elim (ltpss_dx_inv_tpss11 … H ?) -H /2 width=1/ -Hdi #K2 #V2 #HK12 #HV12 #H destruct
       /3 width=8 by aaa_lref/ (**) (* too slow without trace *)
     | elim (lt_or_ge i (d + e)) #Hide
-      [ elim (ltpss_ldrop_conf_be … HL12 … HLK1 ? ?) -L1 // /2 width=2/ #X #H #HLK2
-        elim (ltpss_inv_tpss21 … H ?) -H /2 width=1/ -Hdi -Hide #K2 #V2 #HK12 #HV12 #H destruct
+      [ elim (ltpss_dx_ldrop_conf_be … HL12 … HLK1 ? ?) -L1 // /2 width=2/ #X #H #HLK2
+        elim (ltpss_dx_inv_tpss21 … H ?) -H /2 width=1/ -Hdi -Hide #K2 #V2 #HK12 #HV12 #H destruct
         /3 width=8 by aaa_lref/ (**) (* too slow without trace *)
       | -Hdi
-        lapply (ltpss_ldrop_conf_ge … HL12 … HLK1 ?) -L1 // -Hide
+        lapply (ltpss_dx_ldrop_conf_ge … HL12 … HLK1 ?) -L1 // -Hide
         /3 width=8 by aaa_lref/ (**) (* too slow without trace *)
       ]
     ]
   | * #K2 #V2 #W2 #Hdi #Hide #HLK2 #HVW2 #HWT2
-    elim (ltpss_ldrop_conf_be … HL12 … HLK1 ? ?) -L1 // /2 width=2/ #X #H #HL2K0
-    elim (ltpss_inv_tpss21 … H ?) -H /2 width=1/ -Hdi -Hide #K0 #V0 #HK12 #HV12 #H destruct
+    elim (ltpss_dx_ldrop_conf_be … HL12 … HLK1 ? ?) -L1 // /2 width=2/ #X #H #HL2K0
+    elim (ltpss_dx_inv_tpss21 … H ?) -H /2 width=1/ -Hdi -Hide #K0 #V0 #HK12 #HV12 #H destruct
     lapply (ldrop_mono … HL2K0 … HLK2) -HL2K0 #H destruct
     lapply (ldrop_fwd_ldrop2 … HLK2) -HLK2 #HLK2
     lapply (tpss_trans_eq … HV12 HVW2) -V2 /3 width=7/
@@ -60,12 +61,13 @@ lemma aaa_ltpss_tpss_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2,d,e. L1 ▶* [d
 ]
 qed.
 
-lemma aaa_ltpss_tps_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2,d,e. L1 ▶* [d, e] L2 →
-                          ∀T2. L2 ⊢ T1 ▶ [d, e] T2 → L2 ⊢ T2 ⁝ A.
+lemma aaa_ltpss_dx_tps_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A →
+                             ∀L2,d,e. L1 ▶* [d, e] L2 →
+                             ∀T2. L2 ⊢ T1 ▶ [d, e] T2 → L2 ⊢ T2 ⁝ A.
 /3 width=7/ qed.
 
-lemma aaa_ltpss_conf: ∀L1,T,A. L1 ⊢ T ⁝ A →
-                      ∀L2,d,e. L1 ▶* [d, e] L2 → L2 ⊢ T ⁝ A.
+lemma aaa_ltpss_dx_conf: ∀L1,T,A. L1 ⊢ T ⁝ A →
+                         ∀L2,d,e. L1 ▶* [d, e] L2 → L2 ⊢ T ⁝ A.
 /2 width=7/ qed.
 
 lemma aaa_tpss_conf: ∀L,T1,A. L ⊢ T1 ⁝ A →
diff --git a/matita/matita/contribs/lambda_delta/basic_2/etc/ltpsss/aaa_ltpsss.etc b/matita/matita/contribs/lambda_delta/basic_2/static/aaa_ltpss_sn.ma
similarity index 59%
rename from matita/matita/contribs/lambda_delta/basic_2/etc/ltpsss/aaa_ltpsss.etc
rename to matita/matita/contribs/lambda_delta/basic_2/static/aaa_ltpss_sn.ma
index e3d048809..4f2a44827 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/etc/ltpsss/aaa_ltpsss.etc
+++ b/matita/matita/contribs/lambda_delta/basic_2/static/aaa_ltpss_sn.ma
@@ -12,23 +12,26 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/unfold/ltpsss.ma".
-include "basic_2/static/aaa_ltpss.ma".
+include "basic_2/unfold/ltpss_sn_alt.ma".
+include "basic_2/static/aaa_ltpss_dx.ma".
 
 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
 
-(* Properties about iterated parallel unfold ********************************)
+(* Properties about sn parallel unfold **************************************)
 
-lemma aaa_ltpsss_conf: ∀L1,T,A. L1 ⊢ T ÷ A →
-                       ∀L2,d,e. L1 [d, e] ▶** L2 → L2 ⊢ T ÷ A.
+lemma aaa_ltpss_sn_conf: ∀L1,T,A. L1 ⊢ T ⁝ A →
+                         ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 → L2 ⊢ T ⁝ A.
 #L1 #T #A #HT #L2 #d #e #HL12
-@(TC_Conf3 … (λL,A. L ⊢ T ÷ A) … HT ? HL12) /2 width=5/
+lapply (ltpss_sn_ltpssa … HL12) -HL12 #HL12
+@(TC_Conf3 … (λL,A. L ⊢ T ⁝ A) … HT ? HL12) /2 width=5/
 qed.
 
-lemma aaa_ltpsss_tpss_conf: ∀L1,T1,A. L1 ⊢ T1 ÷ A → ∀L2,d,e. L1 [d, e] ▶** L2 →
-                            ∀T2. L2 ⊢ T1 [d, e] ▶* T2 → L2 ⊢ T2 ÷ A.
+lemma aaa_ltpss_sn_tpss_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A →
+                              ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 →
+                              ∀T2. L2 ⊢ T1 ▶* [d, e] T2 → L2 ⊢ T2 ⁝ A.
 /3 width=5/ qed.
 
-lemma aaa_ltpsss_tps_conf: ∀L1,T1,A. L1 ⊢ T1 ÷ A → ∀L2,d,e. L1 [d, e] ▶** L2 →
-                           ∀T2. L2 ⊢ T1 [d, e] ▶ T2 → L2 ⊢ T2 ÷ A.
+lemma aaa_ltpss_sn_tps_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A →
+                             ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 →
+                             ∀T2. L2 ⊢ T1 ▶ [d, e] T2 → L2 ⊢ T2 ⁝ A.
 /3 width=5/ qed.
diff --git a/matita/matita/contribs/lambda_delta/basic_2/static/ssta_ltpss.ma b/matita/matita/contribs/lambda_delta/basic_2/static/ssta_ltpss_dx.ma
similarity index 69%
rename from matita/matita/contribs/lambda_delta/basic_2/static/ssta_ltpss.ma
rename to matita/matita/contribs/lambda_delta/basic_2/static/ssta_ltpss_dx.ma
index 8af4b30b7..1839c67bd 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/static/ssta_ltpss.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/static/ssta_ltpss_dx.ma
@@ -13,19 +13,19 @@
 (**************************************************************************)
 
 include "basic_2/unfold/tpss_tpss.ma".
-include "basic_2/unfold/ltpss_tpss.ma".
+include "basic_2/unfold/ltpss_dx_tpss.ma".
 include "basic_2/static/ssta_lift.ma".
 
 (* STRATIFIED STATIC TYPE ASSIGNMENT ON TERMS *******************************)
 
-(* Properties about parallel unfold *****************************************)
+(* Properties about dx parallel unfold **************************************)
 
 (* Note: apparently this was missing in basic_1 *)
-lemma ssta_ltpss_tpss_conf: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[g, l] U1 →
-                            ∀L2,d,e. L1 ▶* [d, e] L2 →
-                            ∀T2. L2 ⊢ T1 ▶* [d, e] T2 →
-                            ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g, l] U2 &
-                                  L2 ⊢ U1 ▶* [d, e] U2.
+lemma ssta_ltpss_dx_tpss_conf: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[g, l] U1 →
+                               ∀L2,d,e. L1 ▶* [d, e] L2 →
+                               ∀T2. L2 ⊢ T1 ▶* [d, e] T2 →
+                               ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g, l] U2 &
+                                     L2 ⊢ U1 ▶* [d, e] U2.
 #h #g #L1 #T1 #U #l #H elim H -L1 -T1 -U -l
 [ #L1 #k1 #l1 #Hkl1 #L2 #d #e #_ #T2 #H
   >(tpss_inv_sort1 … H) -H /3 width=3/
@@ -33,27 +33,27 @@ lemma ssta_ltpss_tpss_conf: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[g, l] U1 
   elim (tpss_inv_lref1 … H) -H [ | -HVW1 ]
   [ #H destruct
     elim (lt_or_ge i d) #Hdi [ -HVW1 | ]
-    [ elim (ltpss_ldrop_conf_le … HL12 … HLK1 ?) -L1 /2 width=2/ #X #H #HLK2
-      elim (ltpss_inv_tpss11 … H ?) -H /2 width=1/ #K2 #V2 #HK12 #HV12 #H destruct
+    [ elim (ltpss_dx_ldrop_conf_le … HL12 … HLK1 ?) -L1 /2 width=2/ #X #H #HLK2
+      elim (ltpss_dx_inv_tpss11 … H ?) -H /2 width=1/ #K2 #V2 #HK12 #HV12 #H destruct
       elim (IHVW1 … HK12 … HV12) -IHVW1 -HK12 -HV12 #W2 #HVW2 #HW12
       lapply (ldrop_fwd_ldrop2 … HLK2) #H
       elim (lift_total W2 0 (i+1)) #U2 #HWU2
       lapply (tpss_lift_ge … HW12 … H … HWU1 … HWU2) // -HW12 -H -HWU1
       >minus_plus <plus_minus_m_m // -Hdi /3 width=6/
     | elim (lt_or_ge i (d + e)) #Hide [ -HVW1 | -Hdi -IHVW1 ]
-      [ elim (ltpss_ldrop_conf_be … HL12 … HLK1 ? ?) -L1 // /2 width=2/ #X #H #HLK2
-        elim (ltpss_inv_tpss21 … H ?) -H /2 width=1/ #K2 #V2 #HK12 #HV12 #H destruct
+      [ elim (ltpss_dx_ldrop_conf_be … HL12 … HLK1 ? ?) -L1 // /2 width=2/ #X #H #HLK2
+        elim (ltpss_dx_inv_tpss21 … H ?) -H /2 width=1/ #K2 #V2 #HK12 #HV12 #H destruct
         elim (IHVW1 … HK12 … HV12) -IHVW1 -HK12 -HV12 #W2 #HVW2 #HW12
         lapply (ldrop_fwd_ldrop2 … HLK2) #H
         elim (lift_total W2 0 (i+1)) #U2 #HWU2
         lapply (tpss_lift_ge … HW12 … H … HWU1 … HWU2) // -HW12 -H -HWU1 >minus_plus #H
         lapply (tpss_weak … H d e ? ?) [1,2: normalize [ >commutative_plus <plus_minus_m_m // | /2 width=1/ ]] -Hdi -Hide /3 width=6/
-      | lapply (ltpss_ldrop_conf_ge … HL12 … HLK1 ?) -L1 // -Hide /3 width=6/
+      | lapply (ltpss_dx_ldrop_conf_ge … HL12 … HLK1 ?) -L1 // -Hide /3 width=6/
       ]
     ]
   | * #K2 #V2 #W2 #Hdi #Hide #HLK2 #HVW2 #HWT2
-    elim (ltpss_ldrop_conf_be … HL12 … HLK1 ? ?) -L1 // /2 width=2/ #X #H #HL2K0
-    elim (ltpss_inv_tpss21 … H ?) -H /2 width=1/ #K0 #V0 #HK12 #HV12 #H destruct
+    elim (ltpss_dx_ldrop_conf_be … HL12 … HLK1 ? ?) -L1 // /2 width=2/ #X #H #HL2K0
+    elim (ltpss_dx_inv_tpss21 … H ?) -H /2 width=1/ #K0 #V0 #HK12 #HV12 #H destruct
     lapply (ldrop_mono … HL2K0 … HLK2) -HL2K0 #H destruct
     lapply (ldrop_fwd_ldrop2 … HLK2) -HLK2 #HLK2
     lapply (tpss_trans_eq … HV12 HVW2) -V2 #HV1W2
@@ -67,27 +67,27 @@ lemma ssta_ltpss_tpss_conf: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[g, l] U1 
   elim (tpss_inv_lref1 … H) -H [ | -HWV1 -HWU1 -IHWV1 ]
   [ #H destruct
     elim (lt_or_ge i d) #Hdi [ -HWV1 ]
-    [ elim (ltpss_ldrop_conf_le … HL12 … HLK1 ?) -L1 /2 width=2/ #X #H #HLK2
-      elim (ltpss_inv_tpss11 … H ?) -H /2 width=1/ #K2 #W2 #HK12 #HW12 #H destruct
+    [ elim (ltpss_dx_ldrop_conf_le … HL12 … HLK1 ?) -L1 /2 width=2/ #X #H #HLK2
+      elim (ltpss_dx_inv_tpss11 … H ?) -H /2 width=1/ #K2 #W2 #HK12 #HW12 #H destruct
       elim (IHWV1 … HK12 … HW12) -IHWV1 -HK12 #V2 #HWV2 #_
       lapply (ldrop_fwd_ldrop2 … HLK2) #HLK
       elim (lift_total W2 0 (i+1)) #U2 #HWU2
       lapply (tpss_lift_ge … HW12 … HLK … HWU1 … HWU2) // -HW12 -HLK -HWU1
       >minus_plus <plus_minus_m_m // -Hdi /3 width=6/
     | elim (lt_or_ge i (d + e)) #Hide [ -HWV1 | -IHWV1 -Hdi ]
-      [ elim (ltpss_ldrop_conf_be … HL12 … HLK1 ? ?) -L1 // /2 width=2/ #X #H #HLK2
-        elim (ltpss_inv_tpss21 … H ?) -H /2 width=1/ #K2 #W2 #HK12 #HW12 #H destruct
+      [ elim (ltpss_dx_ldrop_conf_be … HL12 … HLK1 ? ?) -L1 // /2 width=2/ #X #H #HLK2
+        elim (ltpss_dx_inv_tpss21 … H ?) -H /2 width=1/ #K2 #W2 #HK12 #HW12 #H destruct
         elim (IHWV1 … HK12 … HW12) -IHWV1 -HK12 #V2 #HWV2 #_
         lapply (ldrop_fwd_ldrop2 … HLK2) #HLK
         elim (lift_total W2 0 (i+1)) #U2 #HWU2
         lapply (tpss_lift_ge … HW12 … HLK … HWU1 … HWU2) // -HW12 -HLK -HWU1 >minus_plus #H
         lapply (tpss_weak … H d e ? ?) [1,2: normalize [ >commutative_plus <plus_minus_m_m // | /2 width=1/ ]] -Hdi -Hide /3 width=6/
-      | lapply (ltpss_ldrop_conf_ge … HL12 … HLK1 ?) -L1 // -Hide /3 width=6/
+      | lapply (ltpss_dx_ldrop_conf_ge … HL12 … HLK1 ?) -L1 // -Hide /3 width=6/
       ]
     ]
   | * #K2 #V2 #W2 #Hdi #Hide #HLK2 #_ #_
-    elim (ltpss_ldrop_conf_be … HL12 … HLK1 ? ?) -L1 // /2 width=2/ #X #H #HL2K0
-    elim (ltpss_inv_tpss21 … H ?) -H /2 width=1/ -Hdi -Hide #K0 #V0 #_ #_ #H destruct
+    elim (ltpss_dx_ldrop_conf_be … HL12 … HLK1 ? ?) -L1 // /2 width=2/ #X #H #HL2K0
+    elim (ltpss_dx_inv_tpss21 … H ?) -H /2 width=1/ -Hdi -Hide #K0 #V0 #_ #_ #H destruct
     lapply (ldrop_mono … HL2K0 … HLK2) -HL2K0 -HLK2 #H destruct
   ]
 | #a #I #L1 #V1 #T1 #U1 #l #_ #IHTU1 #L2 #d #e #HL12 #X #H
@@ -103,15 +103,16 @@ lemma ssta_ltpss_tpss_conf: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[g, l] U1 
 ]
 qed.
 
-lemma ssta_ltpss_tps_conf: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[g, l] U1 →
-                           ∀L2,d,e. L1 ▶* [d, e] L2 →
-                           ∀T2. L2 ⊢ T1 ▶ [d, e] T2 →
-                           ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g, l] U2 & L2 ⊢ U1 ▶* [d, e] U2.
+lemma ssta_ltpss_dx_tps_conf: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[g, l] U1 →
+                              ∀L2,d,e. L1 ▶* [d, e] L2 →
+                              ∀T2. L2 ⊢ T1 ▶ [d, e] T2 →
+                              ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g, l] U2 &
+			            L2 ⊢ U1 ▶* [d, e] U2.
 /3 width=5/ qed.
 
-lemma ssta_ltpss_conf: ∀h,g,L1,T,U1,l. ⦃h, L1⦄ ⊢ T •[g, l] U1 →
-                       ∀L2,d,e. L1 ▶* [d, e] L2 →
-                       ∃∃U2. ⦃h, L2⦄ ⊢ T •[g, l] U2 & L2 ⊢ U1 ▶* [d, e] U2.
+lemma ssta_ltpss_dx_conf: ∀h,g,L1,T,U1,l. ⦃h, L1⦄ ⊢ T •[g, l] U1 →
+                          ∀L2,d,e. L1 ▶* [d, e] L2 →
+                          ∃∃U2. ⦃h, L2⦄ ⊢ T •[g, l] U2 & L2 ⊢ U1 ▶* [d, e] U2.
 /2 width=5/ qed.
 
 lemma ssta_tpss_conf: ∀h,g,L,T1,U1,l. ⦃h, L⦄ ⊢ T1 •[g, l] U1 →
diff --git a/matita/matita/contribs/lambda_delta/basic_2/static/ssta_ltpss_sn.ma b/matita/matita/contribs/lambda_delta/basic_2/static/ssta_ltpss_sn.ma
new file mode 100644
index 000000000..e8bff44cd
--- /dev/null
+++ b/matita/matita/contribs/lambda_delta/basic_2/static/ssta_ltpss_sn.ma
@@ -0,0 +1,53 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/unfold/ltpss_sn_alt.ma".
+include "basic_2/static/ssta_ltpss_dx.ma".
+
+(* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
+
+(* Properties about sn parallel unfold **************************************)
+
+lemma ssta_ltpss_sn_conf: ∀h,g,L1,T,U1,l. ⦃h, L1⦄ ⊢ T •[g, l] U1 →
+                          ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 →
+                          ∃∃U2. ⦃h, L2⦄ ⊢ T •[g, l] U2 & L1 ⊢ U1 ▶* [d, e] U2.
+#h #g #L1 #T #U1 #l #HTU1 #L2 #d #e #HL12
+lapply (ltpss_sn_ltpssa … HL12) -HL12 #HL12
+@(ltpssa_ind … HL12) -L2 [ /2 width=3/ ] -HTU1
+#L #L2 #HL1 #HL2 * #U #HTU #HU1
+lapply (ltpssa_ltpss_sn … HL1) -HL1 #HL1
+elim (ssta_ltpss_dx_conf … HTU … HL2) -HTU #U2 #HTU2 #HU2
+lapply (ltpss_dx_tpss_trans_eq … HU2 … HL2) -HU2 -HL2 #HU2
+lapply (ltpss_sn_tpss_trans_eq … HU2 … HL1) -HU2 -HL1 #HU2
+lapply (tpss_trans_eq … HU1 HU2) -U /2 width=3/
+qed.
+
+lemma ssta_ltpss_sn_tpss_conf: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[g, l] U1 →
+                               ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 →
+                               ∀T2. L2 ⊢ T1 ▶* [d, e] T2 →
+                               ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g, l] U2 &
+                                     L1 ⊢ U1 ▶* [d, e] U2.
+#h #g #L1 #T1 #U1 #l #HTU1 #L2 #d #e #HL12 #T2 #HT12
+elim (ssta_ltpss_sn_conf … HTU1 … HL12) -HTU1 #U #HT1U #HU1
+elim (ssta_tpss_conf … HT1U … HT12) -T1 #U2 #HTU2 #HU2
+lapply (ltpss_sn_tpss_trans_eq … HU2 … HL12) -HU2 -HL12 #HU2
+lapply (tpss_trans_eq … HU1 HU2) -U /2 width=3/
+qed.
+
+lemma ssta_ltpss_sn_tps_conf: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[g, l] U1 →
+                              ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 →
+                              ∀T2. L2 ⊢ T1 ▶ [d, e] T2 →
+                              ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g, l] U2 &
+                                    L1 ⊢ U1 ▶* [d, e] U2.
+/3 width=3/ qed.
-- 
2.39.2