POPLmark part 1a using the de Bruijn encoding.

[helm.git] / helm / software / matita / contribs / POPLmark / Fsub / part1a.ma

diff --git a/helm/software/matita/contribs/POPLmark/Fsub/part1a.ma b/helm/software/matita/contribs/POPLmark/Fsub/part1a.ma
index 7ae8763cfeddeedaf1c56e1c556ccb203c481362..4ae057be907365ea35af4d02f8a13996f58dbc16 100644 (file)
--- a/helm/software/matita/contribs/POPLmark/Fsub/part1a.ma
+++ b/helm/software/matita/contribs/POPLmark/Fsub/part1a.ma
@@ -50,39 +50,52 @@ theorem narrowing:∀X,G,G1,U,P,M,N.
   G1 ⊢ P ⊴ U → (∀G2,T.G2@G1 ⊢ U ⊴ T → G2@G1 ⊢ P ⊴ T) → G ⊢ M ⊴ N →
   ∀l.G=l@(mk_bound true X U::G1) → l@(mk_bound true X P::G1) ⊢ M ⊴ N.
 intros 10.elim H2
-  [apply SA_Top
-    [rewrite > H5 in H3;
-     apply (WFE_Typ_subst ? ? ? ? ? ? ? H3 (JS_to_WFT1 ? ? ? H))
-    |rewrite > H5 in H4;apply (WFT_env_incl ? ? H4);apply incl_fv_env]
-  |apply SA_Refl_TVar
-    [rewrite > H5 in H3;apply (WFE_Typ_subst ? ? ? ? ? ? ? H3);
-     apply (JS_to_WFT1 ? ? ? H)
-    |rewrite > H5 in H4;rewrite < fv_env_extends;apply H4]
+  [letin x \def fv_env. letin y ≝incl.
+   (* autobatch depth=4 size=8 by SA_Top, WFE_Typ_subst, H3, JS_to_WFT1, H, H4, WFT_env_incl, incl_fv_env]*)
+   apply SA_Top
+    [autobatch by WFE_Typ_subst, H3, JS_to_WFT1, H.
+     (*
+     rewrite > H5 in H3;
+     apply (WFE_Typ_subst ? ? ? ? ? ? ? H3 (JS_to_WFT1 ? ? ? H)) *)
+    |autobatch by H4, WFT_env_incl, incl_fv_env]
+     (* rewrite > H5 in H4;apply (WFT_env_incl ? ? H4);apply incl_fv_env] *)
+  |autobatch depth=4 by SA_Refl_TVar, WFE_Typ_subst, H3, JS_to_WFT1, H, H4. 
+   (*
+   apply SA_Refl_TVar;
+    [autobatch by WFE_Typ_subst, H3, JS_to_WFT1, H.
+    (*
+     rewrite > H5 in H3;apply (WFE_Typ_subst ? ? ? ? ? ? ? H3);
+     apply (JS_to_WFT1 ? ? ? H) *)
+    |autobatch by H4. (* rewrite > H5 in H4;rewrite < fv_env_extends;apply H4*)] *)
   |elim (decidable_eq_nat X n)
     [apply (SA_Trans_TVar ? ? ? P)
       [rewrite < H7;elim l1;simplify
         [constructor 1|constructor 2;assumption]
-      |rewrite > append_cons;apply H1;
-       lapply (WFE_bound_bound true n t1 U ? ? H3)
-        [apply (JS_to_WFE ? ? ? H4)
-        |rewrite < Hletin;rewrite < append_cons;apply (H5 ? H6)
-        |rewrite < H7;rewrite > H6;elim l1;simplify
-          [constructor 1|constructor 2;assumption]]]
-    |apply (SA_Trans_TVar ? ? ? t1)
-      [rewrite > H6 in H3;apply (lookup_env_extends ? ? ? ? ? ? ? ? ? ? H3);
-       unfold;intro;apply H7;symmetry;assumption
+      |applyS H1. 
+       lapply (WFE_bound_bound true n t1 U ? ? H3);
+        [autobatch. (* apply (JS_to_WFE ? ? ? H4) *)
+        |autobatch. (* rewrite < Hletin;rewrite < append_cons;apply (H5 ? H6) *)
+        |destruct.elim l1;autobatch.
+        ]]
+    |(* autobatch depth=4 size=7 by SA_Trans_TVar, lookup_env_extends, H3, sym_neq, H5, H6, H7. *)
+     apply (SA_Trans_TVar ? ? ? t1);
+      [autobatch by lookup_env_extends, H3, sym_neq, H7.
+       (* rewrite > H6 in H3; apply (lookup_env_extends ? ? ? ? ? ? ? ? ? ? H3);
+       unfold;intro;apply H7;symmetry;assumption *)
       |apply (H5 ? H6)]]
-  |apply (SA_Arrow ? ? ? ? ? (H4 ? H7) (H6 ? H7))
-  |apply (SA_All ? ? ? ? ? (H4 ? H7));intros;
+  |autobatch; (* apply (SA_Arrow ? ? ? ? ? (H4 ? H7) (H6 ? H7)) *)
+  |apply (SA_All ? ? ? ? ? (H4 ? H7));intros;autobatch]
+  (* 
    apply (H6 ? ? (mk_bound true X1 t2::l1))
       [rewrite > H7;rewrite > fv_env_extends;apply H8
-      |simplify;rewrite < H7;reflexivity]]
+      |simplify;rewrite < H7;reflexivity]] *)
 qed.
 
 lemma JS_trans_prova: ∀T,G1.WFType G1 T →
 ∀G,R,U.incl ? (fv_env G1) (fv_env G) → G ⊢ R ⊴ T → G ⊢ T ⊴ U → G ⊢ R ⊴ U.
 intros 3;elim H;clear H; try autobatch;
-  [rewrite > (JSubtype_Top ? ? H3);autobatch
+  [
+   rewrite > (JSubtype_Top ? ? H3);autobatch
   |generalize in match H7;generalize in match H4;generalize in match H2;
    generalize in match H5;clear H7 H4 H2 H5;
    generalize in match (refl_eq ? (Arrow t t1));