theory RPCTo

lemma get_echo_int_i_nf:
  "\<forall>s25'.
    \<lbrace>\<lambda>s26'. globals_frame_intact s26' \<and>
            ipc_buffer_valid s26' \<and>
            tls_valid s26' \<and>
            thread_index_C (tls s26') \<in> {1..thread_count} \<and>
            is_valid_w32 s26' (Ptr (symbol_table ''echo_int_i_1'')) \<and>
            is_valid_w32 s26' (Ptr (symbol_table ''echo_int_i_2'')) \<and>
            s26' = s25'\<rbrace>
     get_echo_int_i'
    \<lbrace>\<lambda>r27' s26'. r27' \<in> {Ptr (symbol_table
      ''echo_int_i_1''), Ptr (symbol_table ''echo_int_i_2'')} \<and>
      s26' = s25'\<rbrace>!" apply (rule allI) apply (simp add:get_echo_int_i'_def) apply (wp seL4_GetIPCBuffer_wp) apply (clarsimp simp:thread_count_def tls_valid_def tls_def) apply unat_arith done

(* Proof state trace *)
proof (prove)
goal (1 subgoal):
 1. \<forall>s25'. \<lbrace>\<lambda>s26'. globals_frame_intact s26' \<and> ipc_buffer_valid s26' \<and> tls_valid s26' \<and> thread_index_C (tls s26') \<in> {1..thread_count} \<and> is_valid_w32 s26' (PTR(32 word) (symbol_table ''echo_int_i_1'')) \<and> is_valid_w32 s26' (PTR(32 word) (symbol_table ''echo_int_i_2'')) \<and> s26' = s25'\<rbrace> get_echo_int_i' \<lbrace>\<lambda>r27' s26'. r27' \<in> {PTR(32 signed word) (symbol_table ''echo_int_i_1''), PTR(32 signed word) (symbol_table ''echo_int_i_2'')} \<and> s26' = s25'\<rbrace>! proof (prove)
goal (1 subgoal):
 1. \<And>s25'. \<lbrace>\<lambda>s26'. globals_frame_intact s26' \<and> ipc_buffer_valid s26' \<and> tls_valid s26' \<and> thread_index_C (tls s26') \<in> {1..thread_count} \<and> is_valid_w32 s26' (PTR(32 word) (symbol_table ''echo_int_i_1'')) \<and> is_valid_w32 s26' (PTR(32 word) (symbol_table ''echo_int_i_2'')) \<and> s26' = s25'\<rbrace> get_echo_int_i' \<lbrace>\<lambda>r27' s26'. r27' \<in> {PTR(32 signed word) (symbol_table ''echo_int_i_1''), PTR(32 signed word) (symbol_table ''echo_int_i_2'')} \<and> s26' = s25'\<rbrace>! proof (prove)
goal (1 subgoal):
 1. \<And>s25'. \<lbrace>\<lambda>s26'. globals_frame_intact s26' \<and> ipc_buffer_valid s26' \<and> tls_valid s26' \<and> 1 \<le> thread_index_C (tls s26') \<and> thread_index_C (tls s26') \<le> thread_count \<and> is_valid_w32 s26' (PTR(32 word) (symbol_table ''echo_int_i_1'')) \<and> is_valid_w32 s26' (PTR(32 word) (symbol_table ''echo_int_i_2'')) \<and> s26' = s25'\<rbrace> do ret' <- camkes_get_tls';
y <- guard (\<lambda>s. is_valid_camkes_tls_t_C s ret');
condition (\<lambda>s. thread_index_C (heap_camkes_tls_t_C s ret') = 1)
  (do y <- guard (\<lambda>s. is_valid_w32 s (PTR(32 word) (symbol_table ''echo_int_i_1'')));
return (PTR(32 signed word) (symbol_table ''echo_int_i_1''))
od)
  condition (\<lambda>s. thread_index_C (heap_camkes_tls_t_C s ret') = 2)
  (do y <- guard (\<lambda>s. is_valid_w32 s (PTR(32 word) (symbol_table ''echo_int_i_2'')));
return (PTR(32 signed word) (symbol_table ''echo_int_i_2''))
od)
  (do y <- abort';
fail
od)
od \<lbrace>\<lambda>r27' s26'. (r27' = PTR(32 signed word) (symbol_table ''echo_int_i_1'') \<or> r27' = PTR(32 signed word) (symbol_table ''echo_int_i_2'')) \<and> s26' = s25'\<rbrace>! proof (prove)
goal (1 subgoal):
 1. \<And>s25' s. globals_frame_intact s \<and> ipc_buffer_valid s \<and> tls_valid s \<and> 1 \<le> thread_index_C (tls s) \<and> thread_index_C (tls s) \<le> thread_count \<and> is_valid_w32 s (PTR(32 word) (symbol_table ''echo_int_i_1'')) \<and> is_valid_w32 s (PTR(32 word) (symbol_table ''echo_int_i_2'')) \<and> s = s25' \<Longrightarrow> tls_valid s \<and> globals_frame_intact s \<and> (if thread_index_C (heap_camkes_tls_t_C s (tls_ptr s)) = 1 then ((PTR(32 signed word) (symbol_table ''echo_int_i_1'') = PTR(32 signed word) (symbol_table ''echo_int_i_1'') \<or> PTR(32 signed word) (symbol_table ''echo_int_i_1'') = PTR(32 signed word) (symbol_table ''echo_int_i_2'')) \<and> s = s25') \<and> is_valid_w32 s (PTR(32 word) (symbol_table ''echo_int_i_1'')) else if thread_index_C (heap_camkes_tls_t_C s (tls_ptr s)) = 2 then ((PTR(32 signed word) (symbol_table ''echo_int_i_2'') = PTR(32 signed word) (symbol_table ''echo_int_i_1'') \<or> PTR(32 signed word) (symbol_table ''echo_int_i_2'') = PTR(32 signed word) (symbol_table ''echo_int_i_2'')) \<and> s = s25') \<and> is_valid_w32 s (PTR(32 word) (symbol_table ''echo_int_i_2'')) else False) \<and> is_valid_camkes_tls_t_C s (tls_ptr s) proof (prove)
goal (1 subgoal):
 1. \<And>s25'. \<lbrakk>globals_frame_intact s25'; ipc_buffer_valid s25'; is_valid_camkes_tls_t_C s25' (tls_ptr s25'); 1 \<le> thread_index_C (heap_camkes_tls_t_C s25' (tls_ptr s25')); thread_index_C (heap_camkes_tls_t_C s25' (tls_ptr s25')) \<le> 2; is_valid_w32 s25' (PTR(32 word) (symbol_table ''echo_int_i_1'')); is_valid_w32 s25' (PTR(32 word) (symbol_table ''echo_int_i_2'')); thread_index_C (heap_camkes_tls_t_C s25' (tls_ptr s25')) \<noteq> 2\<rbrakk> \<Longrightarrow> thread_index_C (heap_camkes_tls_t_C s25' (tls_ptr s25')) = 1 proof (prove)
goal:
No subgoals!