X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FPOPLmark%2FFsub%2Fpart1a.ma;h=74ba49240cbe06f6169109e1144c2baaa60a222b;hb=56c4e355b88aa505b64c539053aba92eb86afc2a;hp=8558725cc883569783da832862df8b0d1ed8e969;hpb=ef3e622c49ce8a0478c3ef1326d4f179aff3d1ed;p=helm.git

diff --git a/helm/software/matita/contribs/POPLmark/Fsub/part1a.ma b/helm/software/matita/contribs/POPLmark/Fsub/part1a.ma
index 8558725cc..74ba49240 100644
--- a/helm/software/matita/contribs/POPLmark/Fsub/part1a.ma
+++ b/helm/software/matita/contribs/POPLmark/Fsub/part1a.ma
@@ -12,19 +12,12 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/Fsub/part1a/".
 include "Fsub/defn.ma".
 
 (*** Lemma A.1 (Reflexivity) ***)
-theorem JS_Refl : ∀T,G.WFType G T → WFEnv G → G ⊢ T ⊴  T.
-intros 3.elim H
-  [apply SA_Refl_TVar [apply H2|assumption]
-  |apply SA_Top [assumption|apply WFT_Top]
-  |apply (SA_Arrow ? ? ? ? ? (H2 H5) (H4 H5))
-  |apply (SA_All ? ? ? ? ? (H2 H5));intros;apply (H4 ? H6)
-     [intro;apply H6;apply (fv_WFT ? ? ? (WFT_Forall ? ? ? H1 H3));
-      simplify;autobatch
-     |autobatch]]
+theorem JS_Refl : ∀T,G.(G ⊢ T) → G ⊢ ♦ → G ⊢ T ⊴  T.
+intros 3; elim H;try autobatch;
+apply SA_All; [ autobatch | intros;autobatch depth=4 size=10]
 qed.
 
 (*
@@ -33,102 +26,60 @@ qed.
  * set inclusion.
  *)
 
-lemma JS_weakening : ∀G,T,U.G ⊢ T ⊴ U → ∀H.WFEnv H → incl ? G H → H ⊢ T ⊴ U.
-intros 4;elim H
-  [apply (SA_Top ? ? H4);apply (WFT_env_incl ? ? H2 ? (incl_bound_fv ? ? H5))
-  |apply (SA_Refl_TVar ? ? H4);apply (incl_bound_fv ? ? H5 ? H2)
-  |apply (SA_Trans_TVar ? ? ? ? ? (H3 ? H5 H6));apply H6;assumption
-  |apply (SA_Arrow ? ? ? ? ? (H2 ? H6 H7) (H4 ? H6 H7))
-  |apply (SA_All ? ? ? ? ? (H2 ? H6 H7));intros;apply H4
-     [unfold;intro;apply H8;apply (incl_bound_fv ? ? H7 ? H9)
-     |apply (WFE_cons ? ? ? ? H6 H8);autobatch
-     |unfold;intros;inversion H9;intros
-        [destruct H11;apply in_Base
-        |destruct H13;apply in_Skip;apply (H7 ? H10)]]]
+lemma JS_weakening : ∀G,T,U.G ⊢ T ⊴ U → ∀H.H ⊢ ♦ → G ⊆ H → H ⊢ T ⊴ U.
+intros 4; elim H;try autobatch depth=4 size=7;
+apply (SA_All ? ? ? ? ? (H2 ? H6 H7));
+intros; autobatch depth=6 width=4 size=13;
 qed.
 
+inverter JS_indinv for JSubtype (%?%).
+
 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]
-  |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
-      |apply (H5 ? H6)]]
-  |apply (SA_Arrow ? ? ? ? ? (H4 ? H7) (H6 ? H7))
-  |apply (SA_All ? ? ? ? ? (H4 ? H7));intros;
-   apply (H6 ? ? (mk_bound true X1 t2::l1))
-      [rewrite > H7;rewrite > fv_env_extends;apply H8
-      |simplify;rewrite < H7;reflexivity]]
+  ∀l.G=l@ !X ⊴ U::G1 → l@ !X ⊴ P::G1 ⊢ M ⊴ N.
+intros 10.elim H2; destruct;
+ [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
+      | lapply (WFE_bound_bound X t1 U ? ? H3); autobatch]
+    | apply (SA_Trans_TVar ? ? ? t1); autobatch]
+ | autobatch
+ | apply SA_All;
+    [ autobatch
+    | intros; apply (H6 ? ? (mk_bound true X1 t2::l1)); autobatch]]
 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
-  |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));
-   elim H6 in ⊢ (? ? ? %→%); clear H6; intros; destruct;
-    [apply (SA_Trans_TVar ? ? ? ? H);apply (H4 ? ? H8 H9);autobatch
-    |inversion H11;intros; destruct; autobatch depth=4 width=4 size=9;
-    ]
-  |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 ? (Forall t t1));elim H6 in ⊢ (? ? ? %→%);destruct;
-     [apply (SA_Trans_TVar ? ? ? ? H);apply (H4 ? H7 H8 H9 H10);reflexivity
-     |inversion H11;intros;destruct;
-        [apply SA_Top
-           [autobatch
-              |apply WFT_Forall
-                 [autobatch
-                 |intros;lapply (H4 ? H13);autobatch]]
-           |apply SA_All
-              [autobatch paramodulation
-              |intros;apply (H10 X)
-                 [intro;apply H15;apply H8;assumption
-                 |intro;apply H15;apply H8;apply (WFT_to_incl ? ? ? H3);
-                  assumption
-                 |simplify;autobatch
-                 |apply (narrowing X (mk_bound true X t::l1)
-                         ? ? ? ? ? H7 ? ? [])
-                    [intros;apply H9
-                       [unfold;intros;lapply (H8 ? H17);rewrite > fv_append;
-                        autobatch
-                       |apply (JS_weakening ? ? ? H7)
-                          [autobatch
-                          |unfold;intros;autobatch]
-                       |assumption]
-                    |*:autobatch]
-                 |autobatch]]]]]
+lemma JS_trans_prova: ∀T,G1.(G1 ⊢ T) →
+      ∀G,R,U.fv_env G1 ⊆ fv_env G → G ⊢ R ⊴ T → G ⊢ T ⊴ U → G ⊢ R ⊴ U.
+intros 3;elim H;clear H;
+  [elim H3 using JS_indinv;destruct;autobatch
+  |inversion H3; intros; destruct; assumption
+  |*:elim H6 using JS_indinv;destruct;
+    [1,3: autobatch
+    |*: inversion H7; intros; destruct;
+      [1,2: autobatch depth=4 width=4 size=9
+      | apply SA_Top
+         [ assumption
+         | apply WFT_Forall;intros;autobatch depth=4]
+      | apply SA_All
+         [ autobatch
+         | intros;apply (H4 X);simplify;
+            [4: apply (narrowing X (mk_bound true X t::G) ? ? ? ? ? H11 ? ? [])
+               [intros;apply H2;try unfold;intros;autobatch; 
+               |*:autobatch]
+            |3:apply incl_cons;apply H5
+            |*:autobatch]]]]]
 qed.
 
 theorem JS_trans : ∀G,T,U,V.G ⊢ T ⊴ U → G ⊢ U ⊴ V → G ⊢ T ⊴ V.
-intros 5;apply (JS_trans_prova ? G);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.
+                       G2 @ !X ⊴ Q :: G1 ⊢ T ⊴ U → G1 ⊢ P ⊴ Q →
+                       G2 @ !X ⊴ P :: G1 ⊢ T ⊴ U.
 intros;apply (narrowing ? ? ? ? ? ? ? H1 ? H) [|autobatch]
-intros;apply (JS_trans ? ? ? ? ? H2);apply (JS_weakening ? ? ? H1);
-     [autobatch|unfold;intros;autobatch]
-qed.
+intros;apply (JS_trans ? ? ? ? ? H2);apply (JS_weakening ? ? ? H1);autobatch.
+qed.
\ No newline at end of file