reorganization of the "static" component:

[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 56eebf47ccc5fcd4e9948ce2ba585b59a0e7f64e..e25a5902def0f261ef4ae1ecacee3ff1af1ea717 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_aaa.ma
@@ -20,59 +20,64 @@ include "basic_2/reduction/lpx_ldrop.ma".
 
 (* 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.
-#h #g #L1 #T1 #A #H elim H -L1 -T1 -A
-[ #L1 #k #X #H
+(* Note: lemma 500 *)
+lemma cpx_lpx_aaa_conf: ∀h,g,G,L1,T1,A. ⦃G, L1⦄ ⊢ T1 ⁝ A →
+                        ∀T2. ⦃G, L1⦄ ⊢ T1 ➡[h, g] T2 →
+                        ∀L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 → ⦃G, L2⦄ ⊢ T2 ⁝ A.
+#h #g #G #L1 #T1 #A #H elim H -G -L1 -T1 -A
+[ #g #L1 #k #X #H
   elim (cpx_inv_sort1 … H) -H // * //
-| #I #L1 #K1 #V1 #B #i #HLK1 #_ #IHV1 #X #H #L2 #HL12
+| #I #G #L1 #K1 #V1 #B #i #HLK1 #_ #IHV1 #X #H #L2 #HL12
   elim (cpx_inv_lref1 … H) -H
   [ #H destruct
     elim (lpx_ldrop_conf … HLK1 … HL12) -L1 #X #H #HLK2
-    elim (lpx_inv_pair1 … H) -H #K2 #V2 #HK12 #HV12 #H destruct /3 width=6/
+    elim (lpx_inv_pair1 … H) -H
+    #K2 #V2 #HK12 #HV12 #H destruct /3 width=6 by aaa_lref/
   | * #J #Y #Z #V2 #H #HV12 #HV2
     lapply (ldrop_mono … H … HLK1) -H #H destruct
     elim (lpx_ldrop_conf … HLK1 … HL12) -L1 #Z #H #HLK2
     elim (lpx_inv_pair1 … H) -H #K2 #V0 #HK12 #_ #H destruct
-    lapply (ldrop_fwd_ldrop2 … HLK2) -V0 /3 width=7/
+    /3 width=8 by aaa_lift, ldrop_fwd_drop2/
   ]
-| #a #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
+| #a #G #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
   elim (cpx_inv_abbr1 … H) -H *
-  [ #V2 #T2 #HV12 #HT12 #H destruct /4 width=2/
+  [ #V2 #T2 #HV12 #HT12 #H destruct /4 width=2 by lpx_pair, aaa_abbr/
   | #T2 #HT12 #HT2 #H destruct -IHV1
-    @(aaa_inv_lift (L2.ⓓV1) … HT2) -HT2 /2 width=1/ /3 width=1/
+    /4 width=8 by lpx_pair, aaa_inv_lift, ldrop_drop/
   ]
-| #a #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
-  elim (cpx_inv_abst1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /4 width=1/
-| #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
+| #a #G #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
+  elim (cpx_inv_abst1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
+  /4 width=1 by lpx_pair, aaa_abst/
+| #G #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
+  [ #V2 #T2 #HV12 #HT12 #H destruct /3 width=3 by aaa_appl/
+  | #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 by cpx_bind/ -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/
+    /5 width=6 by lsuba_aaa_trans, lsuba_abbr, aaa_abbr, aaa_cast/
   | #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
-    elim (aaa_inv_abbr … H) -H /3 width=3/
+    lapply (aaa_lift G L2 … B … (L2.ⓓW2) … HV2) -HV2 /2 width=2 by ldrop_drop/ #HV2
+    lapply (IHT1 (ⓓ{b}W2.U2) … HL12) -IHT1 /2 width=1 by cpx_bind/ -L1 #H
+    elim (aaa_inv_abbr … H) -H /3 width=3 by aaa_abbr, aaa_appl/
   ]
-| #L1 #V1 #T1 #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
+| #G #L1 #V1 #T1 #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
   elim (cpx_inv_cast1 … H) -H
-  [ * #V2 #T2 #HV12 #HT12 #H destruct /3 width=1/
-  | -IHV1 /2 width=1/
+  [ * #V2 #T2 #HV12 #HT12 #H destruct /3 width=1 by aaa_cast/
+  | -IHV1 /2 width=1 by/
+  | -IHT1 /2 width=1 by/
   ]
 ]
 qed-.
 
-lemma aaa_cpx_conf: ∀h,g,L,T1,A. L ⊢ T1 ⁝ A → ∀T2. ⦃h, L⦄ ⊢ T1 ➡[g] T2 → L ⊢ T2 ⁝ A.
-/2 width=7 by aaa_cpx_lpx_conf/ qed-.
+lemma cpx_aaa_conf: ∀h,g,G,L,T1,A. ⦃G, L⦄ ⊢ T1 ⁝ A → ∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 → ⦃G, L⦄ ⊢ T2 ⁝ A.
+/2 width=7 by cpx_lpx_aaa_conf/ qed-.
 
-lemma aaa_lpx_conf: ∀h,g,L1,T,A. L1 ⊢ T ⁝ A → ∀L2. ⦃h, L1⦄ ⊢ ➡[g] L2 → L2 ⊢ T ⁝ A.
-/2 width=7 by aaa_cpx_lpx_conf/ qed-.
+lemma lpx_aaa_conf: ∀h,g,G,L1,T,A. ⦃G, L1⦄ ⊢ T ⁝ A → ∀L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 → ⦃G, L2⦄ ⊢ T ⁝ A.
+/2 width=7 by cpx_lpx_aaa_conf/ qed-.
 
-lemma aaa_cpr_conf: ∀L,T1,A. L ⊢ T1 ⁝ A → ∀T2. L ⊢ T1 ➡ T2 → L ⊢ T2 ⁝ A.
-/3 width=5 by aaa_cpx_conf, cpr_cpx/ qed-.
+lemma cpr_aaa_conf: ∀G,L,T1,A. ⦃G, L⦄ ⊢ T1 ⁝ A → ∀T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L⦄ ⊢ T2 ⁝ A.
+/3 width=5 by cpx_aaa_conf, cpr_cpx/ qed-.
 
-lemma aaa_lpr_conf: ∀L1,T,A. L1 ⊢ T ⁝ A → ∀L2. L1 ⊢ ➡ L2 → L2 ⊢ T ⁝ A.
-/3 width=5 by aaa_lpx_conf, lpr_lpx/ qed-.
+lemma lpr_aaa_conf: ∀G,L1,T,A. ⦃G, L1⦄ ⊢ T ⁝ A → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ T ⁝ A.
+/3 width=5 by lpx_aaa_conf, lpr_lpx/ qed-.