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: âR. reflexive ? R â
âL1,L2. lpx (TC ⦠R) L1 L2 â 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: âR,K1,K2. lpx R K1 K2 â âL1,L2. lpx R L1 L2 â
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: âL1,T1,A. L1 ⢠T1 â A â âL2,d,e. L1 â¶* [d, e] L2 â
- âT2. L2 ⢠T1 â¶* [d, e] T2 â L2 ⢠T2 â A.
+lemma aaa_ltpss_dx_tpss_conf: âL1,T1,A. L1 ⢠T1 â A â
+ âL2,d,e. L1 â¶* [d, e] L2 â
+ âT2. L2 ⢠T1 â¶* [d, e] T2 â L2 ⢠T2 â 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: âL1,T1,A. L1 ⢠T1 â A â âL2,d,e. L1 â¶* [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: âL1,T1,A. L1 ⢠T1 â A â âL2,d,e. L1 â¶* [d
]
qed.
-lemma aaa_ltpss_tps_conf: âL1,T1,A. L1 ⢠T1 â A â âL2,d,e. L1 â¶* [d, e] L2 â
- âT2. L2 ⢠T1 ⶠ[d, e] T2 â L2 ⢠T2 â A.
+lemma aaa_ltpss_dx_tps_conf: âL1,T1,A. L1 ⢠T1 â A â
+ âL2,d,e. L1 â¶* [d, e] L2 â
+ âT2. L2 ⢠T1 ⶠ[d, e] T2 â L2 ⢠T2 â A.
/3 width=7/ qed.
-lemma aaa_ltpss_conf: âL1,T,A. L1 ⢠T â A â
- âL2,d,e. L1 â¶* [d, e] L2 â L2 ⢠T â A.
+lemma aaa_ltpss_dx_conf: âL1,T,A. L1 ⢠T â A â
+ âL2,d,e. L1 â¶* [d, e] L2 â L2 ⢠T â A.
/2 width=7/ qed.
lemma aaa_tpss_conf: âL,T1,A. L ⢠T1 â A â
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: âL1,T,A. L1 ⢠T ÷ A â
- âL2,d,e. L1 [d, e] â¶** L2 â L2 ⢠T ÷ A.
+lemma aaa_ltpss_sn_conf: âL1,T,A. L1 ⢠T â A â
+ âL2,d,e. L1 ⢠â¶* [d, e] L2 â L2 ⢠T â 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 â A) ⦠HT ? HL12) /2 width=5/
qed.
-lemma aaa_ltpsss_tpss_conf: âL1,T1,A. L1 ⢠T1 ÷ A â âL2,d,e. L1 [d, e] â¶** L2 â
- âT2. L2 ⢠T1 [d, e] â¶* T2 â L2 ⢠T2 ÷ A.
+lemma aaa_ltpss_sn_tpss_conf: âL1,T1,A. L1 ⢠T1 â A â
+ âL2,d,e. L1 ⢠â¶* [d, e] L2 â
+ âT2. L2 ⢠T1 â¶* [d, e] T2 â L2 ⢠T2 â A.
/3 width=5/ qed.
-lemma aaa_ltpsss_tps_conf: âL1,T1,A. L1 ⢠T1 ÷ A â âL2,d,e. L1 [d, e] â¶** L2 â
- âT2. L2 ⢠T1 [d, e] ⶠT2 â L2 ⢠T2 ÷ A.
+lemma aaa_ltpss_sn_tps_conf: âL1,T1,A. L1 ⢠T1 â A â
+ âL2,d,e. L1 ⢠â¶* [d, e] L2 â
+ âT2. L2 ⢠T1 ⶠ[d, e] T2 â L2 ⢠T2 â 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: âh,g,L1,T1,U1,l. â¦h, L1⦠⢠T1 â¢[g, l] U1 â
- âL2,d,e. L1 â¶* [d, e] L2 â
- âT2. L2 ⢠T1 â¶* [d, e] T2 â
- ââU2. â¦h, L2⦠⢠T2 â¢[g, l] U2 &
- L2 ⢠U1 â¶* [d, e] U2.
+lemma ssta_ltpss_dx_tpss_conf: âh,g,L1,T1,U1,l. â¦h, L1⦠⢠T1 â¢[g, l] U1 â
+ âL2,d,e. L1 â¶* [d, e] L2 â
+ âT2. L2 ⢠T1 â¶* [d, e] T2 â
+ ââU2. â¦h, L2⦠⢠T2 â¢[g, l] U2 &
+ L2 ⢠U1 â¶* [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: âh,g,L1,T1,U1,l. â¦h, L1⦠⢠T1 â¢[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: âh,g,L1,T1,U1,l. â¦h, L1⦠⢠T1 â¢[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: âh,g,L1,T1,U1,l. â¦h, L1⦠⢠T1 â¢[g, l] U1
]
qed.
-lemma ssta_ltpss_tps_conf: âh,g,L1,T1,U1,l. â¦h, L1⦠⢠T1 â¢[g, l] U1 â
- âL2,d,e. L1 â¶* [d, e] L2 â
- âT2. L2 ⢠T1 ⶠ[d, e] T2 â
- ââU2. â¦h, L2⦠⢠T2 â¢[g, l] U2 & L2 ⢠U1 â¶* [d, e] U2.
+lemma ssta_ltpss_dx_tps_conf: âh,g,L1,T1,U1,l. â¦h, L1⦠⢠T1 â¢[g, l] U1 â
+ âL2,d,e. L1 â¶* [d, e] L2 â
+ âT2. L2 ⢠T1 ⶠ[d, e] T2 â
+ ââU2. â¦h, L2⦠⢠T2 â¢[g, l] U2 &
+ L2 ⢠U1 â¶* [d, e] U2.
/3 width=5/ qed.
-lemma ssta_ltpss_conf: âh,g,L1,T,U1,l. â¦h, L1⦠⢠T â¢[g, l] U1 â
- âL2,d,e. L1 â¶* [d, e] L2 â
- ââU2. â¦h, L2⦠⢠T â¢[g, l] U2 & L2 ⢠U1 â¶* [d, e] U2.
+lemma ssta_ltpss_dx_conf: âh,g,L1,T,U1,l. â¦h, L1⦠⢠T â¢[g, l] U1 â
+ âL2,d,e. L1 â¶* [d, e] L2 â
+ ââU2. â¦h, L2⦠⢠T â¢[g, l] U2 & L2 ⢠U1 â¶* [d, e] U2.
/2 width=5/ qed.
lemma ssta_tpss_conf: âh,g,L,T1,U1,l. â¦h, L⦠⢠T1 â¢[g, l] U1 â
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: âh,g,L1,T,U1,l. â¦h, L1⦠⢠T â¢[g, l] U1 â
+ âL2,d,e. L1 ⢠â¶* [d, e] L2 â
+ ââU2. â¦h, L2⦠⢠T â¢[g, l] U2 & L1 ⢠U1 â¶* [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: âh,g,L1,T1,U1,l. â¦h, L1⦠⢠T1 â¢[g, l] U1 â
+ âL2,d,e. L1 ⢠â¶* [d, e] L2 â
+ âT2. L2 ⢠T1 â¶* [d, e] T2 â
+ ââU2. â¦h, L2⦠⢠T2 â¢[g, l] U2 &
+ L1 ⢠U1 â¶* [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: âh,g,L1,T1,U1,l. â¦h, L1⦠⢠T1 â¢[g, l] U1 â
+ âL2,d,e. L1 ⢠â¶* [d, e] L2 â
+ âT2. L2 ⢠T1 ⶠ[d, e] T2 â
+ ââU2. â¦h, L2⦠⢠T2 â¢[g, l] U2 &
+ L1 ⢠U1 â¶* [d, e] U2.
+/3 width=3/ qed.
--
2.39.5