maybe good?

cs3234/labs/term-project.v

@@ -724,6 +724,26 @@ Definition specification_of_run (run : target_program -> expressible_value) :=
        fetch_decode_execute_loop bcis nil = KO s ->
        run (Target_program bcis) = Expressible_msg s).
 
+
+Theorem there_is_at_most_one_run_function :
+  forall (f g : target_program -> expressible_value),
+    specification_of_run f ->
+    specification_of_run g ->
+    forall (t: target_program),
+    f t = g t.
+Proof.
+  intros f g.
+  unfold specification_of_run.
+  intros S_f S_g [bcis].
+  case (fetch_decode_execute_loop bcis nil) as [ds | s] eqn:H_fdel.
+  - destruct (S_f fetch_decode_execute_loop fetch_decode_execute_loop_satifies_the_specification) as [S_f_nil _].
+    destruct (S_g fetch_decode_execute_loop fetch_decode_execute_loop_satifies_the_specification) as [S_g_nil _].
+    case ds as [ | n ds' ] eqn:H_ds.
+    + rewrite -> (S_g_nil bcis H_fdel).
+      exact (S_f_nil bcis H_fdel).
+    + Check (S_f_nil bcis).
+
+
 (* Task 4:
    a. time permitting, prove that the definition above specifies at most one function;
    b. implement this function; and