--- /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/equivalence/cpcs_cpcs.ma".
+include "basic_2/dynamic/lsubsv.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
+
+(* Properties on context-sensitive parallel equivalence for terms ***********)
+
+lemma lsubsv_cpcs_trans: ∀h,g,L1,L2. h ⊢ L1 ⊩:⊑[g] L2 →
+ ∀T1,T2. L2 ⊢ T1 ⬌* T2 → L1 ⊢ T1 ⬌* T2.
+/3 width=5 by lsubsv_fwd_lsubs2, cpcs_lsubs_trans/
+qed-.
(**************************************************************************)
include "basic_2/dynamic/lsubsv_ldrop.ma".
+include "basic_2/dynamic/lsubsv_cpcs.ma".
(*
include "basic_2/dynamic/lsubsv_ssta.ma".
-include "basic_2/dynamic/lsubsv_cpcs.ma".
*)
(* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
/3 width=3 by lsubsv_fwd_lsubss, lsubss_xprs_trans/ qed-.
*)
-axiom lsubsv_snv_trans: ∀h,g,L2,T. ⦃h, L2⦄ ⊩ T :[g] →
+lemma lsubsv_snv_trans: ∀h,g,L2,T. ⦃h, L2⦄ ⊩ T :[g] →
∀L1. h ⊢ L1 ⊩:⊑[g] L2 → ⦃h, L1⦄ ⊩ T :[g].
-(*
#h #g #L2 #T #H elim H -L2 -T //
-[ #I2 #L2 #K2 #V2 #i #HLK2 #_ #IHV2 #L1 #HL12
+[ #I2 #L2 #K2 #W2 #i #HLK2 #_ #IHW2 #L1 #HL12
elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
- elim (lsubsv_inv_pair2 … H) -H * #K1 [ | -IHV2 ]
+ elim (lsubsv_inv_pair2 … H) -H * #K1 [ | -IHW2 ]
[ #HK12 #H destruct /3 width=5/
- | #V1 #l #HV1 #_ #_ #_ #H destruct /2 width=5/
+ | #W1 #V1 #l #HV1 #_ #_ #_ #_ #H #_ destruct /2 width=5/
]
| #a #I #L2 #V #T #_ #_ #IHV #IHT #L1 #HL12 /4 width=1/
| #a #L2 #V #W #W0 #T #U #l #_ #_ #HVW #HW0 #HTU #IHV #IHT #L1 #HL12
lapply (IHV … HL12) -IHV #HV
lapply (IHT … HL12) -IHT #HT
- lapply (lsubsv_ssta_trans … HVW … HL12) -HVW #HVW
lapply (lsubsv_cprs_trans … HL12 … HW0) -HW0 #HW0
+(*
+ lapply (lsubsv_ssta_trans … HVW … HL12) -HVW #HVW
lapply (lsubsv_xprs_trans … HL12 … HTU) -HL12 -HTU /2 width=8/
-| #L2 #W #T #U #l #_ #_ #HTU #HWU #IHW #IHT #L1 #HL12
+*)
+| #L2 #W #T #U #l #_ #_ #HTU #HUW #IHW #IHT #L1 #HL12
lapply (IHW … HL12) -IHW #HW
lapply (IHT … HL12) -IHT #HT
+ lapply (lsubsv_cpcs_trans … HL12 … HUW) -HUW #HUW
+(*
lapply (lsubsv_ssta_trans … HTU … HL12) -HTU #HTU
- lapply (lsubsv_cpcs_trans … HL12 … HWU) -HL12 -HWU /2 width=4/
+-HL12 -HWU /2 width=4/
]
qed-.
*)
--- /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/equivalence/cpcs_cpcs.ma".
+include "basic_2/dynamic/lsubsv_ldrop.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
+
+(* Properties on stratified native type assignment **************************)
+
+lemma lsubsv_ssta_trans: ∀h,g,L2,T,U2,l. ⦃h, L2⦄ ⊢ T •[g,l] U2 →
+ ∀L1. h ⊢ L1 ⊩:⊑[g] L2 →
+ ∃∃U1. L1 ⊢ U2 ⬌* U1 & ⦃h, L1⦄ ⊢ T •[g,l] U1.
+#h #g #L2 #T #U2 #l #H elim H -L2 -T -U2 -l
+[ #L2 #k #l #Hkl #L1 #_ /3 width=3/
+| #L2 #K2 #V2 #W2 #U2 #i #l #HLK2 #_ #HWU2 #IHVW2 #L1 #HL12
+ elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
+ elim (lsubsv_inv_pair2 … H) -H *
+ [ #K1 #HK12 #H destruct
+ elim (IHVW2 … HK12) -K2 #W1 #HW21 #H
+ elim (lift_total W1 0 (i+1)) #U1 #HWU1
+ lapply (ldrop_fwd_ldrop2 … HLK1) /3 width=9/
+ | #K1 #V1 #W1 #l0 #_ #_ #_ #_ #_ #_ #H destruct
+ ]
+| #L2 #K2 #W2 #V2 #U2 #i #l #HLK2 #_ #HWU2 #IHWV2 #L1 #HL12
+ elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
+ elim (lsubsv_inv_pair2 … H) -H *
+ [ #K1 #HK12 #H destruct
+ elim (IHWV2 … HK12) -K2 #V1 #_ #H -V2 /3 width=6/
+ | #K1 #W1 #V1 #l0 #HV1 #HVW1 #HW21 #HW2 #HK12 #H #_ destruct
+ elim (IHWV2 … HK12) -K2 #V #_ #H
+ elim (lift_total W1 0 (i+1)) #U1 #HWU1
+ lapply (ldrop_fwd_ldrop2 … HLK1) #HLK
+ @(ex2_intro … U1)
+ [ @(cpcs_lift … HLK … HWU2 … HWU1 HW21)
+ | @(ssta_ldef … HLK1 … HWU1)
+ (*
+ /3 width=9/
+ *)
\ No newline at end of file
lapply (IH1 … HT20 … (L2.ⓛW20) … HT202) [1,2: /2 width=1/ ] -IH1 -HT20 -HT202 #HT2
elim (IH3 … HVW1 … HL12 … HV12) // [2: /2 width=1/ ] -HV1 -HVW1 -HV12 #W200 #HVW200 #H
lapply (cpcs_trans … HW210 … H) -W10 #HW200
+(*
lapply (lsubsv_snv_trans … HT2 (L2.ⓓV2) ?) -L1 -HT2 /2 width=1/ /2 width=4/
- |
\ No newline at end of file
+ |
+*)
\ No newline at end of file
+++ /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/equivalence/cpcs_cpcs.ma".
-include "basic_2/dynamic/lsubsv.ma".
-
-(* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
-
-(* Properties on context-sensitive parallel equivalence for terms ***********)
-
-lemma lsubsv_cpcs_trans: ∀h,g,L1,L2. h ⊢ L1 ⊩:⊑[g] L2 →
- ∀T1,T2. L2 ⊢ T1 ⬌* T2 → L1 ⊢ T1 ⬌* T2.
-/3 width=5 by lsubsv_fwd_lsubs2, cpcs_lsubs_trans/
-qed-.
+++ /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/computation/xprs_lsubss.ma".
-include "basic_2/dynamic/lsubsv.ma".
-
-(* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
-
-(* Properties on stratified native type assignment **************************)
-
-axiom lsubsv_ssta_trans: ∀h,g,L2,T,U2,l. ⦃h, L2⦄ ⊢ T •[g,l] U2 →
- ∀L1. h ⊢ L1 ⊩:⊑[g] L2 →
- ∃∃U1. L1 ⊢ U2 ⬌* U1 & ⦃h, L1⦄ ⊢ T •[g,l] U1.
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