- the substitution lemma is proved!

[helm.git] / matita / matita / contribs / lambda-delta / Basic-2 / substitution / tps_tps.ma

diff --git a/matita/matita/contribs/lambda-delta/Basic-2/substitution/tps_tps.ma b/matita/matita/contribs/lambda-delta/Basic-2/substitution/tps_tps.ma
index a969da023b5017619e839c5a6d6e7724dc7b691d..3daf6fbe2d4fc1f78a0ca476ee97a041ecaf9b98 100644 (file)
--- a/matita/matita/contribs/lambda-delta/Basic-2/substitution/tps_tps.ma
+++ b/matita/matita/contribs/lambda-delta/Basic-2/substitution/tps_tps.ma
@@ -33,10 +33,11 @@ theorem tps_conf_eq: ∀L,T0,T1,d1,e1. L ⊢ T0 [d1, e1] ≫ T1 →
   ]
 | #L #I #V0 #V1 #T0 #T1 #d1 #e1 #_ #_ #IHV01 #IHT01 #X #d2 #e2 #HX
   elim (tps_inv_bind1 … HX) -HX #V2 #T2 #HV02 #HT02 #HX destruct -X;
+  lapply (tps_leq_repl_dx … HT02 (L. 𝕓{I} V1) ?) -HT02 /2/ #HT02  
   elim (IHV01 … HV02) -IHV01 HV02 #V #HV1 #HV2
   elim (IHT01 … HT02) -IHT01 HT02 #T #HT1 #HT2
-  lapply (tps_leq_repl … HT1 (L. 𝕓{I} V1) ?) -HT1 /2/
-  lapply (tps_leq_repl … HT2 (L. 𝕓{I} V2) ?) -HT2 /3 width=5/
+  lapply (tps_leq_repl_dx … HT1 (L. 𝕓{I} V) ?) -HT1 /2/
+  lapply (tps_leq_repl_dx … HT2 (L. 𝕓{I} V) ?) -HT2 /3 width=5/
 | #L #I #V0 #V1 #T0 #T1 #d1 #e1 #_ #_ #IHV01 #IHT01 #X #d2 #e2 #HX
   elim (tps_inv_flat1 … HX) -HX #V2 #T2 #HV02 #HT02 #HX destruct -X;
   elim (IHV01 … HV02) -IHV01 HV02;
@@ -70,8 +71,8 @@ theorem tps_conf_neq: ∀L1,T0,T1,d1,e1. L1 ⊢ T0 [d1, e1] ≫ T1 →
   elim (IHV01 … HV02 H) -IHV01 HV02 #V #HV1 #HV2
   elim (IHT01 … HT02 ?) -IHT01 HT02
   [ -H #T #HT1 #HT2
-    lapply (tps_leq_repl … HT1 (L2. 𝕓{I} V1) ?) -HT1 /2/
-    lapply (tps_leq_repl … HT2 (L1. 𝕓{I} V2) ?) -HT2 /3 width=5/
+    lapply (tps_leq_repl_dx … HT1 (L2. 𝕓{I} V) ?) -HT1 /2/
+    lapply (tps_leq_repl_dx … HT2 (L1. 𝕓{I} V) ?) -HT2 /3 width=5/
   | -HV1 HV2 >plus_plus_comm_23 >plus_plus_comm_23 in ⊢ (? ? %) elim H -H #H
     [ @or_introl | @or_intror ] /2 by monotonic_le_plus_l/ (**) (* /3/ is too slow *)
   ]
@@ -93,23 +94,14 @@ theorem tps_trans_down: ∀L,T1,T0,d1,e1. L ⊢ T1 [d1, e1] ≫ T0 →
   <(tps_inv_lift1_eq … HWT2 … HVW) -HWT2 /4/
 | #L #I #V1 #V0 #T1 #T0 #d1 #e1 #_ #_ #IHV10 #IHT10 #X #d2 #e2 #HX #de2d1
   elim (tps_inv_bind1 … HX) -HX #V2 #T2 #HV02 #HT02 #HX destruct -X;
-  lapply (tps_leq_repl … HT02 (L. 𝕓{I} V1) ?) -HT02 /2/ #HT02
+  lapply (tps_leq_repl_dx … HT02 (L. 𝕓{I} V0) ?) -HT02 /2/ #HT02
   elim (IHV10 … HV02 ?) -IHV10 HV02 // #V
   elim (IHT10 … HT02 ?) -IHT10 HT02 [2: /2/ ] #T #HT1 #HT2
-  lapply (tps_leq_repl … HT2 (L. 𝕓{I} V) ?) -HT2 /3 width=6/
+  lapply (tps_leq_repl_dx … HT1 (L. 𝕓{I} V) ?) -HT1;
+  lapply (tps_leq_repl_dx … HT2 (L. 𝕓{I} V2) ?) -HT2 /3 width=6/
 | #L #I #V1 #V0 #T1 #T0 #d1 #e1 #_ #_ #IHV10 #IHT10 #X #d2 #e2 #HX #de2d1
   elim (tps_inv_flat1 … HX) -HX #V2 #T2 #HV02 #HT02 #HX destruct -X;
   elim (IHV10 … HV02 ?) -IHV10 HV02 //
   elim (IHT10 … HT02 ?) -IHT10 HT02 // /3 width=6/
 ]
 qed.
-(*
-      Theorem subst0_subst0: (t1,t2,u2:?; j:?) (subst0 j u2 t1 t2) ->
-                             (u1,u:?; i:?) (subst0 i u u1 u2) ->
-                             (EX t | (subst0 j u1 t1 t) & (subst0 (S (plus i j)) u t t2)).
-
-      Theorem subst0_subst0_back: (t1,t2,u2:?; j:?) (subst0 j u2 t1 t2) ->
-                                  (u1,u:?; i:?) (subst0 i u u2 u1) ->
-                                  (EX t | (subst0 j u1 t1 t) & (subst0 (S (plus i j)) u t2 t)).
-
-*)