milestone update in basic_2, update in ground and static_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx_fsle.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx_fsle.ma
index d26a5d55767b823bbc4d23a628655c8c4bb2d8de..d4769c8385ce58e634a184bbb7699f5845714aad 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx_fsle.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx_fsle.ma
@@ -15,21 +15,23 @@
 include "static_2/static/fsle_drops.ma".
 include "static_2/static/rex_fsle.ma".
 include "basic_2/rt_transition/rpx_length.ma".
+include "basic_2/rt_transition/rpx_drops.ma".
 include "basic_2/rt_transition/rpx_fqup.ma".
 
 (* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
 
 (* Forward lemmas with free variables inclusion for restricted closures *****)
 
-(* Note: "⦃L2, T1⦄ ⊆ ⦃L2, T0⦄" does not hold *)
-(* Note: Take L0 = K0.ⓓ(ⓝW.V), L2 = K0.ⓓW, T0 = #0, T1 = ⬆*[1]V *)
-(* Note: This invalidates rpxs_cpx_conf: "∀h,G. s_r_confluent1 … (cpx h G) (rpxs h G)" *)
-lemma rpx_cpx_conf_fsge (h) (G): ∀L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈[h] T1 →
-                                 ∀L2. ⦃G, L0⦄ ⊢⬈[h, T0] L2 → ⦃L2, T1⦄ ⊆ ⦃L0, T0⦄.
-#h #G0 #L0 #T0 @(fqup_wf_ind_eq (Ⓕ) … G0 L0 T0) -G0 -L0 -T0
+(* Note: "❪L2, T1❫ ⊆ ❪L2, T0❫" does not hold *)
+(* Note: Take L0 = K0.ⓓ(ⓝW.V), L2 = K0.ⓓW, T0 = #0, T1 = ⇧[1]V *)
+(* Note: This invalidates rpxs_cpx_conf: "∀G. s_r_confluent1 … (cpx G) (rpxs G)" *)
+lemma rpx_cpx_conf_fsge (G):
+      ∀L0,T0,T1. ❪G,L0❫ ⊢ T0 ⬈ T1 →
+      ∀L2. ❪G,L0❫ ⊢⬈[T0] L2 → ❪L2,T1❫ ⊆ ❪L0,T0❫.
+#G0 #L0 #T0 @(fqup_wf_ind_eq (Ⓣ) … G0 L0 T0) -G0 -L0 -T0
 #G #L #T #IH #G0 #L0 * *
-[ #s #HG #HL #HT #X #HX #Y #HY destruct -IH
-  elim (cpx_inv_sort1 … HX) -HX #H destruct
+[ #s0 #HG #HL #HT #X #HX #Y #HY destruct -IH
+  elim (cpx_inv_sort1 … HX) -HX #s1 #H destruct
   lapply (rpx_fwd_length … HY) -HY #H0
   /2 width=1 by fsle_sort_bi/
 | * [| #i ] #HG #HL #HT #X #HX #Y #HY destruct
@@ -72,9 +74,10 @@ lemma rpx_cpx_conf_fsge (h) (G): ∀L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈[h] T1 →
   [ #V1 #T1 #HV01 #HT01 #H destruct
     lapply (rpx_fwd_length … HV0) #H0
     /4 width=6 by fsle_bind_eq, fsle_fwd_pair_sn/
-  | #T #HT #HXT #H1 #H2 destruct
+  | #T #H2T0 #HTX #H1 #H2 destruct
+    lapply (rpx_inv_lifts_bi … HT0 (Ⓣ) … H2T0) -HT0 [6:|*: /3 width=2 by drops_refl, drops_drop/ ] #HT
     lapply (rpx_fwd_length … HV0) #H0
-    /3 width=8 by fsle_inv_lifts_sn/
+    /5 width=6 by fsle_bind_dx_dx, fsle_lifts_dx, fqup_zeta/
   ]
 | #I #V0 #X0 #HG #HL #HT #X #HX #Y #HY destruct
   elim (rex_inv_flat … HY) -HY #HV0 #HX0
@@ -111,26 +114,27 @@ lemma rpx_cpx_conf_fsge (h) (G): ∀L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈[h] T1 →
 ]
 qed-.
 
-lemma rpx_fsge_comp (h) (G): rex_fsge_compatible (cpx h G).
+lemma rpx_fsge_comp (G): rex_fsge_compatible (cpx G).
 /2 width=4 by rpx_cpx_conf_fsge/ qed-.
 
 (**) (* this section concerns cpx *)
 (* Properties with generic extension on referred entries ********************)
 
 (* Basic_2A1: uses: cpx_frees_trans *)
-lemma cpx_fsge_comp (h) (G): R_fsge_compatible (cpx h G).
+lemma cpx_fsge_comp (G): R_fsge_compatible (cpx G).
 /2 width=4 by rpx_cpx_conf_fsge/ qed-.
 
 (* Note: lemma 1000 *)
 (* Basic_2A1: uses: cpx_llpx_sn_conf *)
-lemma cpx_rex_conf (R) (h) (G): s_r_confluent1 … (cpx h G) (rex R).
+lemma cpx_rex_conf (R) (G): s_r_confluent1 … (cpx G) (rex R).
 /3 width=3 by fsge_rex_trans, cpx_fsge_comp/ qed-.
 
 (* Advanced properties ******************************************************)
 
-lemma rpx_cpx_conf (h) (G): s_r_confluent1 … (cpx h G) (rpx h G).
+lemma rpx_cpx_conf (G): s_r_confluent1 … (cpx G) (rpx G).
 /2 width=5 by cpx_rex_conf/ qed-.
 
-lemma rpx_cpx_conf_fsge_dx (h) (G): ∀L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈[h] T1 →
-                                    ∀L2. ⦃G, L0⦄ ⊢⬈[h, T0] L2 → ⦃L2, T1⦄ ⊆ ⦃L0, T1⦄.
+lemma rpx_cpx_conf_fsge_dx (G):
+      ∀L0,T0,T1. ❪G,L0❫ ⊢ T0 ⬈ T1 →
+      ∀L2. ❪G,L0❫ ⊢⬈[T0] L2 → ❪L2,T1❫ ⊆ ❪L0,T1❫.
 /3 width=5 by rpx_cpx_conf, rpx_fsge_comp/ qed-.