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[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 b113769ddf042c01de9461b28df7fe999692cdbc..9e097b279cab5a032eea7735d1b334a5c471ff28 100644 (file)
--- a/helm/software/matita/contribs/POPLmark/Fsub/part1a.ma
+++ b/helm/software/matita/contribs/POPLmark/Fsub/part1a.ma
@@ -14,10 +14,8 @@
 
 include "Fsub/defn.ma".
 
-axiom daemon : False.
-
 (*** Lemma A.1 (Reflexivity) ***)
-theorem JS_Refl : ∀T,G.WFType G T → WFEnv G → G ⊢ T ⊴  T.
+theorem JS_Refl : ∀T,G.(G ⊢ T) → G ⊢ ♦ → G ⊢ T ⊴  T.
 intros 3; elim H;
  [1,2,3: autobatch
  | apply SA_All; [ autobatch | intros;autobatch depth=4 size=10]]
@@ -29,7 +27,7 @@ qed.
  * set inclusion.
  *)
 
-lemma JS_weakening : ∀G,T,U.G ⊢ T ⊴ U → ∀H.WFEnv H → incl ? G H → H ⊢ T ⊴ U.
+lemma JS_weakening : ∀G,T,U.G ⊢ T ⊴ U → ∀H.H ⊢ ♦ → G ⊆ H → H ⊢ T ⊴ U.
 intros 4; elim H;
  [1,2,3,4: autobatch depth=4 size=7
  | apply (SA_All ? ? ? ? ? (H2 ? H6 H7));
@@ -40,14 +38,14 @@ 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.
+  ∀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 true X t1 U ? ? H3); autobatch]
+      | lapply (WFE_bound_bound X t1 U ? ? H3); autobatch]
     | apply (SA_Trans_TVar ? ? ? t1); autobatch]
  | autobatch
  | apply SA_All;
@@ -55,8 +53,8 @@ intros 10.elim H2; destruct;
     | 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.
+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
@@ -73,6 +71,7 @@ intros 3;elim H;clear H;
             [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.
 
@@ -81,8 +80,8 @@ 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.
 qed.