More automation

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));

diff --git a/helm/software/matita/contribs/POPLmark/Fsub/part1a_inversion3.ma b/helm/software/matita/contribs/POPLmark/Fsub/part1a_inversion3.ma
index 16f38322a9c6cc830c39c2d0f9ca10ef2b2ce9fa..0f32da3495a805abaf39e369fce863957393c3e2 100644 (file)
--- a/helm/software/matita/contribs/POPLmark/Fsub/part1a_inversion3.ma
+++ b/helm/software/matita/contribs/POPLmark/Fsub/part1a_inversion3.ma
@@ -18,12 +18,8 @@ include "Fsub/defn2.ma".
 theorem JS_Refl : ∀T,G.WFType G T → WFEnv G → G ⊢ T ⊴  T.
 intros 3; elim H;
  [1,2,3: autobatch
- | apply SA_All;
-    [ autobatch
-    | intros; apply (H4 ? H6);
-       [ intro; apply H6; apply (fv_WFT ? ? ? (WFT_Forall ? ? ? H1 H3));
-         simplify; autobatch
-       | autobatch]]]
+ | apply SA_All; [ autobatch | intros; autobatch depth=4 size=10]
+ ]
 qed.
 
 (*
@@ -34,12 +30,9 @@ qed.
 
 lemma JS_weakening : ∀G,T,U.G ⊢ T ⊴ U → ∀H.WFEnv H → incl ? G H → H ⊢ T ⊴ U.
 intros 4; elim H;
- [1,2,3,4: autobatch depth=4 width=4 size=7
- | apply (SA_All ? ? ? ? ? (H2 ? H6 H7));intros;
-   apply H4
-     [ intro; autobatch
-     | apply WFE_cons; autobatch
-     | unfold;intros; elim (in_list_cons_case ? ? ? ? H9); destruct; autobatch]]
+ [1,2,3,4: autobatch depth=4 size=7
+ | apply (SA_All ? ? ? ? ? (H2 ? H6 H7));
+   intros; apply H4; autobatch depth=4 size=7]
 qed.
 
 lemma JSubtype_inv:
@@ -57,34 +50,25 @@ lemma JSubtype_inv:
  intros;
  generalize in match (refl_eq ? T);
  generalize in match (refl_eq ? G);
- elim H5 in ⊢ (? ? ? % → ? ? ? % → %); destruct; 
-  [1,2,3,4: autobatch depth=10 width=10 size=8
-  | apply H4; first [assumption | autobatch]]
+ elim H5 in ⊢ (? ? ? % → ? ? ? % → %); destruct; autobatch depth=3 width=4 size=7;
 qed.
 
 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; destruct;
- [1,2,4: autobatch width=10 depth=10 size=8
+ [letin x \def fv_env. letin y ≝incl. autobatch depth=4 size=8.
+ | autobatch depth=4 size=7;
  | elim (decidable_eq_nat X n)
     [apply (SA_Trans_TVar ? ? ? P); destruct;
       [ autobatch
       | rewrite > append_cons; apply H1;
-        lapply (WFE_bound_bound true X t1 U ? ? H3); destruct;
-          [1,3: autobatch
-          | rewrite < append_cons; autobatch
-          ]]
-    | apply (SA_Trans_TVar ? ? ? t1)
-      [ apply (lookup_env_extends ? ? ? ? ? ? ? ? ? ? H3);
-        intro; autobatch
-      | autobatch]]
+        lapply (WFE_bound_bound true X t1 U ? ? H3); destruct;autobatch]
+    | apply (SA_Trans_TVar ? ? ? t1); autobatch]
+ | autobatch
  | apply SA_All;
     [ autobatch
-    | intros;
-      apply (H6 ? ? (mk_bound true X1 t2::l1))
-      [ rewrite > fv_env_extends; autobatch
-      | autobatch]]]
+    | intros; apply (H6 ? ? (mk_bound true X1 t2::l1));autobatch]]
 qed.
 
 lemma JS_trans_prova: ∀T,G1.WFType G1 T →
@@ -100,35 +84,29 @@ intros 3;elim H;clear H; try autobatch;
          [ assumption
          | apply WFT_Forall;
             [ autobatch
-            | intros;lapply (H8 ? H11);
-              autobatch]]
+            | intros;autobatch depth =4]]
       | apply SA_All
          [ autobatch
          | intros;apply (H4 X);
-            [intro; autobatch;
-            |intro;  apply H13;apply H5; apply (WFT_to_incl ? ? ? H3);
-             assumption
-            |simplify;autobatch
+            [intro; autobatch 
+            |intro; autobatch depth=4.  
+            |simplify; autobatch
             |apply (narrowing X (mk_bound true X t::G) ? ? ? ? ? H9 ? ? [])
                [intros;apply H2
-                  [unfold;intros;lapply (H5 ? H15);rewrite > fv_append;
-                   autobatch
-                  |apply (JS_weakening ? ? ? H9)
-                     [autobatch
-                     |unfold;intros;autobatch]
+                  [unfold;intros;lapply (H5 ? H15);rewrite > fv_append;autobatch
+                  |autobatch
                   |assumption]
                |*:autobatch]
             |autobatch]]]]]
 qed.
 
 theorem JS_trans : ∀G,T,U,V.G ⊢ T ⊴ U → G ⊢ U ⊴ V → G ⊢ T ⊴ V.
-intros 5; autobatch.
+intros 5; apply (JS_trans_prova ? G); autobatch depth=2.
 qed.
 
 theorem JS_narrow : ∀G1,G2,X,P,Q,T,U.
                        (G2 @ (mk_bound true X Q :: G1)) ⊢ T ⊴ U → G1 ⊢ P ⊴ Q →
                        (G2 @ (mk_bound true X P :: G1)) ⊢ T ⊴ U.
-intros; apply (narrowing ? ? ? ? ? ? ? H1 ? H) [|autobatch]
-intros;apply (JS_trans ? ? ? ? ? H2);apply (JS_weakening ? ? ? H1);
-     [autobatch|unfold;intros;autobatch]
+intros;apply (narrowing ? ? ? ? ? ? ? H1 ? H) [|autobatch]
+intros;apply (JS_trans ? ? ? ? ? H2);apply (JS_weakening ? ? ? H1);autobatch.
 qed.