Typo fixed.

[helm.git] / helm / software / matita / library / assembly / test.ma

diff --git a/helm/software/matita/library/assembly/test.ma b/helm/software/matita/library/assembly/test.ma
index 11cc0e4e7e785eaf2c1195a59fc35cd23e966272..644cebaa9d57d3edb1182e63a4fc164faba9a4e2 100644 (file)
--- a/helm/software/matita/library/assembly/test.ma
+++ b/helm/software/matita/library/assembly/test.ma
@@ -132,8 +132,7 @@ lemma loop_invariant':
       rewrite < minus_n_O;
       normalize in ⊢ (? ? (? (? ? %) ?) ?);
       change in ⊢ (? ? % ?) with (update (mult_memory x y) 32 〈x0, x0〉 a);
-      change in ⊢ (? ? ? %) with (update (update (update (mult_memory x y) 30 x) 31
-        (byte_of_nat y)) 32 (byte_of_nat 0) a);
+      simplify in ⊢ (? ? ? %);
       change in ⊢ (? ? ? (? (? (? ? ? %) ? ?) ? ? ?)) with (mult_memory x y 30);
       rewrite > byte_of_nat_nat_of_byte;
       change in ⊢ (? ? ? (? (? ? ? %) ? ? ?)) with (mult_memory x y 31);
@@ -145,34 +144,19 @@ lemma loop_invariant':
       reflexivity
     ]
   | cut (5 + 23 * S n = 5 + 23 * n + 23);
-    [ letin K ≝ (breakpoint (mult_status x y) (5 + 23 * n) 23); clearbody K;
-      letin H' ≝ (H ?); clearbody H'; clear H;
-      [ apply le_S_S_to_le;
+    [ rewrite > Hcut; clear Hcut;
+      rewrite > breakpoint;
+      rewrite > H; clear H;
+      [2: apply le_S_S_to_le;
         apply le_S;
         apply H1
-      | letin xxx ≝ (eq_f ? ? (λz. execute (mult_status x y) z) ? ? Hcut); clearbody xxx;
-        clear Hcut;
-        rewrite > xxx;
-        clear xxx;
-        apply (transitive_eq ? ? ? ? K);
-        clear K; 
-        rewrite > H';
-        clear H';
-        cut (∃z.y-n=S z ∧ z < 255);
+      | cut (∃z.y-n=S z ∧ z < 255);
          [ elim Hcut; clear Hcut;
            elim H; clear H;
            rewrite > H2;
            (* instruction LDAd *)
-           letin K ≝
-            (breakpoint
-              (mk_status (byte_of_nat (x*n)) 4 O
-               (eqbyte 〈x0, x0〉 (byte_of_nat (x*n)))
-               (plusbytec (byte_of_nat (x*pred n)) x)
-               (update (update (update (mult_memory x y) 30 x) 31 (byte_of_nat (S a))) 32
-               (byte_of_nat (x*n))) O)
-              3 20); clearbody K;
-           normalize in K:(? ? (? ? %) ?);
-           rewrite > K; clear K;
+           change in ⊢ (? ? (? ? %) ?) with (3+20);
+           rewrite > breakpoint in ⊢ (? ? % ?);
            whd in ⊢ (? ? (? % ?) ?);
            normalize in ⊢ (? ? (? (? ? % ? ? ? ? ?) ?) ?);
            change in ⊢ (? ? (? (? % ? ? ? ? ? ?) ?) ?)
@@ -180,28 +164,22 @@ lemma loop_invariant':
            change in ⊢ (? ? (? (? ? ? ? (? ? %) ? ? ?) ?) ?) with
             (byte_of_nat (S a));
            (* instruction BEQ *)
-           letin K ≝
-            (breakpoint
-              (mk_status (byte_of_nat (S a)) 6 O
-               (eqbyte 〈x0, x0〉 (byte_of_nat (S a)))
-               (plusbytec (byte_of_nat (x*pred n)) x)
-                (update (update (update (mult_memory x y) 30 x) 31 (byte_of_nat (S a))) 32
-                 (byte_of_nat (x*n))) O)
-              3 17); clearbody K;
-           normalize in K:(? ? (? ? %) ?);
-           rewrite > K; clear K;
+           change in ⊢ (? ? (? ? %) ?) with (3+17);
+           rewrite > breakpoint in ⊢ (? ? % ?);
            whd in ⊢ (? ? (? % ?) ?);
            letin K ≝ (eq_eqbyte_x0_x0_byte_of_nat_S_false ? H3); clearbody K;
            rewrite > K; clear K;
            simplify in ⊢ (? ? (? (? ? % ? ? ? ? ?) ?) ?);
            (* instruction LDAd *)
-           rewrite > (breakpoint ? 3 14);
+           change in ⊢ (? ? (? ? %) ?) with (3+14);
+           rewrite > breakpoint in ⊢ (? ? % ?);
            whd in ⊢ (? ? (? % ?) ?);
            change in ⊢ (? ? (? (? % ? ? ? ? ? ?) ?) ?) with (byte_of_nat (x*n));
            normalize in ⊢ (? ? (? (? ? % ? ? ? ? ?) ?) ?);
            change in ⊢ (? ? (? (? ? ? ? % ? ? ?) ?) ?) with (eqbyte 〈x0, x0〉 (byte_of_nat (x*n)));
            (* instruction DECd *)
-           rewrite > (breakpoint ? 5 9);
+           change in ⊢ (? ? (? ? %) ?) with (5+9);
+           rewrite > breakpoint in ⊢ (? ? % ?);
            whd in ⊢ (? ? (? % ?) ?);
            change in ⊢ (? ? (? (? ? ? ? (? ? %) ? ? ?) ?) ?) with (bpred (byte_of_nat (S a)));
            rewrite > (eq_bpred_S_a_a ? H3);
@@ -213,7 +191,8 @@ lemma loop_invariant':
                 reflexivity | ];
            rewrite < Hcut; clear Hcut; clear H3; clear H2; clear a;          
            (* instruction ADDd *)
-           rewrite > (breakpoint ? 3 6);
+           change in ⊢ (? ? (? ? %) ?) with (3+6);
+           rewrite > breakpoint in ⊢ (? ? % ?);
            whd in ⊢ (? ? (? % ?) ?);
            change in ⊢ (? ? (? (? % ? ? ? ? ? ?) ?) ?) with
             (plusbytenc (byte_of_nat (x*n)) x);
@@ -233,26 +212,14 @@ lemma loop_invariant':
            rewrite < pred_Sn;        
            apply status_eq;
             [1,2,3,4,7: normalize; reflexivity
-            | change with (plusbytec (byte_of_nat (x*n)) x =
-                             plusbytec (byte_of_nat (x*n)) x);
+            | change with (plusbytec #(x*n) x = plusbytec #(x*n) x);
               reflexivity
             |6: intro;
               simplify in ⊢ (? ? ? %);
+              normalize in ⊢ (? ? (? (? ? ? ? ? ? (? ? (? %) ?) ?) ?) ?);
               change in ⊢ (? ? % ?) with
-               (update
-                (update
-                 (update
-                  (update (update (mult_memory x y) 30 x) 31
-                   (byte_of_nat (S (nat_of_byte y-S n)))) 32 (byte_of_nat (nat_of_byte x*n))) 31
-                    (byte_of_nat (nat_of_byte y-S n)))
-                   (nat_of_byte
-                    (update
-                     (update
-                      (update (update (mult_memory x y) 30 x) 31
-                       (byte_of_nat (S (nat_of_byte y-S n)))) 32 (byte_of_nat (nat_of_byte x*n))) 31
-                      (byte_of_nat (nat_of_byte y-S n)) 15))
-                     (byte_of_nat (nat_of_byte x*S n)) a);
-              normalize in ⊢ (? ? (? ? % ? ?) ?);
+               ((mult_memory x y){30↦x}{31↦#(S (y-S n))}{32↦#(x*n)}{31↦#(y-S n)}
+                {〈x2,x0〉↦ #(x*S n)} a);
               apply inj_update;
               intro;
               apply inj_update;
@@ -270,7 +237,11 @@ lemma loop_invariant':
                  apply (minus_Sn_m (nat_of_byte y) (S n) H1)
                | letin K ≝ (lt_nat_of_byte_256 y); clearbody K;
                  letin K' ≝ (lt_minus_m y (S n) ? ?); clearbody K';
-                 autobatch
+                 [ apply (lt_to_le_to_lt O (S n) (nat_of_byte y) ? ?);
+                   autobatch
+                 | autobatch
+                 | autobatch
+                 ]
                ]
             ]
          ]
@@ -306,16 +277,13 @@ theorem test_x_y:
        apply status_eq;
         [1,2,3,4,5,7: normalize; reflexivity
         | intro;
-        letin xxx \def ((mult_memory x y) { a ↦ x }).
-          change with (update (update (update (mult_memory x y) 30 x) 31 (byte_of_nat O)) 32
-(byte_of_nat (nat_of_byte x*nat_of_byte y)) a =
-           update (update (mult_memory x y) 31 〈x0, x0〉) 32
+          simplify in ⊢ (? ? ? %);
+          change in ⊢ (? ? % ?) with
+           (update (update (update (mult_memory x y) 30 x) 31 (byte_of_nat O)) 32
 (byte_of_nat (nat_of_byte x*nat_of_byte y)) a);
-          apply inj_update; intro;
-          apply inj_update; intro;
-          change in ⊢ (? ? (? ? ? % ?) ?) with (mult_memory x y 30);
-          apply eq_update_s_a_sa
+          repeat (apply inj_update; intro);
+          apply (eq_update_s_a_sa ? 30)
         ]
      ]
   ].
-qed.
+qed.
\ No newline at end of file