partial commit: just the components before "static" ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / lpx_aaa.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_aaa.ma
index 3863f7bb54f655e9d1458946d70b005659c47a9e..41d1386ddc2b9d7ee4a9af1af356016534799bb1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_aaa.ma
@@ -16,12 +16,13 @@ include "basic_2/static/aaa_lift.ma".
 include "basic_2/static/lsuba_aaa.ma".
 include "basic_2/reduction/lpx_ldrop.ma".
 
-(* SN PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS *****************************)
+(* SN EXTENDED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ********************)
 
 (* Properties on atomic arity assignment for terms **************************)
 
-lemma aaa_cpx_lpx_conf: ∀h,g,L1,T1,A. L1 ⊢ T1 ⁝ A → ∀T2. ⦃h, L1⦄ ⊢ T1 ➡[g] T2 →
-                        ∀L2. ⦃h, L1⦄ ⊢ ➡[g] L2 → L2 ⊢ T2 ⁝ A.
+(* Note: lemma 500 *)
+lemma aaa_cpx_lpx_conf: ∀h,g,L1,T1,A. L1 ⊢ T1 ⁝ A → ∀T2. ⦃h, L1⦄ ⊢ T1 ➡[h, g] T2 →
+                        ∀L2. ⦃h, L1⦄ ⊢ ➡[h, g] L2 → L2 ⊢ T2 ⁝ A.
 #h #g #L1 #T1 #A #H elim H -L1 -T1 -A
 [ #L1 #k #X #H
   elim (cpx_inv_sort1 … H) -H // * //
@@ -47,11 +48,11 @@ lemma aaa_cpx_lpx_conf: ∀h,g,L1,T1,A. L1 ⊢ T1 ⁝ A → ∀T2. ⦃h, L1⦄ 
 | #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
   elim (cpx_inv_appl1 … H) -H *
   [ #V2 #T2 #HV12 #HT12 #H destruct /3 width=3/
-  | #b #V2 #W1 #U1 #U2 #HV12 #HU12 #H1 #H2 destruct
+  | #b #V2 #W1 #W2 #U1 #U2 #HV12 #HW12 #HU12 #H1 #H2 destruct
     lapply (IHV1 … HV12 … HL12) -IHV1 -HV12 #HV2
-    lapply (IHT1 (ⓛ{b}W1.U2) … HL12) -IHT1 /2 width=1/ -L1 #H
+    lapply (IHT1 (ⓛ{b}W2.U2) … HL12) -IHT1 /2 width=1/ -L1 #H
     elim (aaa_inv_abst … H) -H #B0 #A0 #HW1 #HU2 #H destruct
-    lapply (lsuba_aaa_trans … HU2 (L2.ⓓV2) ?) -HU2 /2 width=2/ /2 width=3/
+    lapply (lsuba_aaa_trans … HU2 (L2.ⓓⓝW2.V2) ?) -HU2 /3 width=3/
   | #b #V #V2 #W1 #W2 #U1 #U2 #HV1 #HV2 #HW12 #HU12 #H1 #H2 destruct
     lapply (aaa_lift L2 … B … (L2.ⓓW2) … HV2) -HV2 /2 width=1/ #HV2
     lapply (IHT1 (ⓓ{b}W2.U2) … HL12) -IHT1 /2 width=1/ -L1 #H
@@ -61,17 +62,18 @@ lemma aaa_cpx_lpx_conf: ∀h,g,L1,T1,A. L1 ⊢ T1 ⁝ A → ∀T2. ⦃h, L1⦄ 
   elim (cpx_inv_cast1 … H) -H
   [ * #V2 #T2 #HV12 #HT12 #H destruct /3 width=1/
   | -IHV1 /2 width=1/
+  | -IHT1 /2 width=1/
   ]
 ]
 qed-.
 
-lemma aaa_cpx_conf: ∀h,g,L,T1,A. L ⊢ T1 ⁝ A → ∀T2. ⦃h, L⦄ ⊢ T1 ➡[g] T2 → L ⊢ T2 ⁝ A.
+lemma aaa_cpx_conf: ∀h,g,L,T1,A. ⦃G, L⦄ ⊢ T1 ⁝ A → ∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 → ⦃G, L⦄ ⊢ T2 ⁝ A.
 /2 width=7 by aaa_cpx_lpx_conf/ qed-.
 
-lemma aaa_lpx_conf: ∀h,g,L1,T,A. L1 ⊢ T ⁝ A → ∀L2. ⦃h, L1⦄ ⊢ ➡[g] L2 → L2 ⊢ T ⁝ A.
+lemma aaa_lpx_conf: ∀h,g,L1,T,A. L1 ⊢ T ⁝ A → ∀L2. ⦃h, L1⦄ ⊢ ➡[h, g] L2 → L2 ⊢ T ⁝ A.
 /2 width=7 by aaa_cpx_lpx_conf/ qed-.
 
-lemma aaa_cpr_conf: ∀L,T1,A. L ⊢ T1 ⁝ A → ∀T2. L ⊢ T1 ➡ T2 → L ⊢ T2 ⁝ A.
+lemma aaa_cpr_conf: ∀L,T1,A. ⦃G, L⦄ ⊢ T1 ⁝ A → ∀T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L⦄ ⊢ T2 ⁝ A.
 /3 width=5 by aaa_cpx_conf, cpr_cpx/ qed-.
 
 lemma aaa_lpr_conf: ∀L1,T,A. L1 ⊢ T ⁝ A → ∀L2. L1 ⊢ ➡ L2 → L2 ⊢ T ⁝ A.