milestone update in basic_2, update in ground and static_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_aaa.ma
index 6f4b3b2a0949b060167cd2bd4ead040d78d039f2..2652783e75b3a5808526519377569143d9aa628d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_aaa.ma
@@ -12,53 +12,58 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/static/aaa_lift.ma".
-include "basic_2/static/lsuba_aaa.ma".
-include "basic_2/reduction/lpx_drop.ma".
+include "static_2/static/aaa_drops.ma".
+include "static_2/static/lsuba_aaa.ma".
+include "basic_2/rt_transition/lpx_drops.ma".
 
-(* SN EXTENDED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ********************)
+(* EXTENDED PARALLEL RT-TRANSITION FOR FULL LOCAL ENVIRONMENTS **************)
 
-(* Properties on atomic arity assignment for terms **************************)
+(* Properties with atomic arity assignment for terms ************************)
 
 (* Note: lemma 500 *)
-lemma cpx_lpx_aaa_conf: ∀h,o,G,L1,T1,A. ⦃G, L1⦄ ⊢ T1 ⁝ A →
-                        ∀T2. ⦃G, L1⦄ ⊢ T1 ➡[h, o] T2 →
-                        ∀L2. ⦃G, L1⦄ ⊢ ➡[h, o] L2 → ⦃G, L2⦄ ⊢ T2 ⁝ A.
-#h #o #G #L1 #T1 #A #H elim H -G -L1 -T1 -A
-[ #o #L1 #s #X #H
-  elim (cpx_inv_sort1 … H) -H // * //
-| #I #G #L1 #K1 #V1 #B #i #HLK1 #_ #IHV1 #X #H #L2 #HL12
-  elim (cpx_inv_lref1 … H) -H
-  [ #H destruct
-    elim (lpx_drop_conf … HLK1 … HL12) -L1 #X #H #HLK2
-    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 (drop_mono … H … HLK1) -H #H destruct
-    elim (lpx_drop_conf … HLK1 … HL12) -L1 #Z #H #HLK2
-    elim (lpx_inv_pair1 … H) -H #K2 #V0 #HK12 #_ #H destruct
-    /3 width=8 by aaa_lift, drop_fwd_drop2/
+(* Basic_2A1: was: cpx_lpx_aaa_conf *)
+lemma cpx_aaa_conf_lpx (G) (L1):
+      ∀T1,A. ❪G,L1❫ ⊢ T1 ⁝ A →
+      ∀T2. ❪G,L1❫ ⊢ T1 ⬈ T2 →
+      ∀L2. ❪G,L1❫ ⊢ ⬈ L2 → ❪G,L2❫ ⊢ T2 ⁝ A.
+#G #L1 #T1 #A #H elim H -G -L1 -T1 -A
+[ #G #L1 #s1 #X #H
+  elim (cpx_inv_sort1 … H) -H #s2 #H destruct //
+| #I #G #K1 #V1 #B #_ #IH #X #HX #Y #HY
+  elim (lpx_inv_pair_sn … HY) -HY #K2 #V2 #HK12 #HV12 #H destruct
+  elim (cpx_inv_zero1_pair … HX) -HX
+  [ #H destruct /3 width=1 by aaa_zero/
+  | * #V #HV1 #HVX -HV12
+    /4 width=7 by aaa_lifts, drops_refl, drops_drop, true/
   ]
-| #a #G #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
+| #I1 #G #K1 #A #i #_ #IH #X #HX #Y #HY
+  elim (lpx_inv_bind_sn … HY) -HY #I2 #K2 #HK12 #_ #H destruct
+  elim (cpx_inv_lref1_bind … HX) -HX
+  [ #H destruct /3 width=1 by aaa_lref/
+  | * #T #HT #HTX
+    /4 width=7 by aaa_lifts, drops_refl, drops_drop, true/
+  ]
+| #p #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 by lpx_pair, aaa_abbr/
-  | #T2 #HT12 #HT2 #H destruct -IHV1
-    /4 width=8 by lpx_pair, aaa_inv_lift, drop_drop/
+  | #X1 #HXT1 #HX1 #H destruct -IHV1
+    elim (cpx_lifts_sn … HX1 (Ⓣ) … (L1.ⓓV1) … HXT1) -X1
+    /4 width=7 by lpx_pair, aaa_inv_lifts, drops_refl, drops_drop/
   ]
-| #a #G #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
+| #p #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 by aaa_appl/
-  | #b #V2 #W1 #W2 #U1 #U2 #HV12 #HW12 #HU12 #H1 #H2 destruct
+  | #q #V2 #W1 #W2 #U1 #U2 #HV12 #HW12 #HU12 #H1 #H2 destruct
     lapply (IHV1 … HV12 … HL12) -IHV1 -HV12 #HV2
-    lapply (IHT1 (ⓛ{b}W2.U2) … HL12) -IHT1 /2 width=1 by cpx_bind/ -L1 #H
+    lapply (IHT1 (ⓛ[q]W2.U2) … HL12) -IHT1 /2 width=1 by cpx_bind/ -L1 #H
     elim (aaa_inv_abst … H) -H #B0 #A0 #HW1 #HU2 #H destruct
     /5 width=6 by lsuba_aaa_trans, lsuba_beta, aaa_abbr, aaa_cast/
-  | #b #V #V2 #W1 #W2 #U1 #U2 #HV1 #HV2 #HW12 #HU12 #H1 #H2 destruct
-    lapply (aaa_lift G L2 … B … (L2.ⓓW2) … HV2) -HV2 /2 width=2 by drop_drop/ #HV2
-    lapply (IHT1 (ⓓ{b}W2.U2) … HL12) -IHT1 /2 width=1 by cpx_bind/ -L1 #H
+  | #q #V #V2 #W1 #W2 #U1 #U2 #HV1 #HV2 #HW12 #HU12 #H1 #H2 destruct
+    lapply (aaa_lifts G L2 … B … (L2.ⓓW2) … HV2) -HV2 /3 width=2 by drops_refl, drops_drop/ #HV2
+    lapply (IHT1 (ⓓ[q]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/
   ]
 | #G #L1 #V1 #T1 #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
@@ -70,14 +75,9 @@ lemma cpx_lpx_aaa_conf: ∀h,o,G,L1,T1,A. ⦃G, L1⦄ ⊢ T1 ⁝ A →
 ]
 qed-.
 
-lemma cpx_aaa_conf: ∀h,o,G,L,T1,A. ⦃G, L⦄ ⊢ T1 ⁝ A → ∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, o] T2 → ⦃G, L⦄ ⊢ T2 ⁝ A.
-/2 width=7 by cpx_lpx_aaa_conf/ qed-.
-
-lemma lpx_aaa_conf: ∀h,o,G,L1,T,A. ⦃G, L1⦄ ⊢ T ⁝ A → ∀L2. ⦃G, L1⦄ ⊢ ➡[h, o] L2 → ⦃G, L2⦄ ⊢ T ⁝ A.
-/2 width=7 by cpx_lpx_aaa_conf/ 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 cpx_aaa_conf (G) (L): Conf3 … (aaa G L) (cpx G L).
+/2 width=7 by cpx_aaa_conf_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-.
+lemma lpx_aaa_conf (G):
+      ∀T. Conf3 … (λL. aaa G L T) (lpx G).
+/2 width=7 by cpx_aaa_conf_lpx/ qed-.