theory RPCTo

lemma get_echo_char_i_nf:
  "\<forall>s34'.
    \<lbrace>\<lambda>s35'. globals_frame_intact s35' \<and>
            ipc_buffer_valid s35' \<and>
            tls_valid s35' \<and>
            thread_index_C (tls s35') \<in> {1..thread_count} \<and>
            is_valid_w8 s35' (Ptr (symbol_table ''echo_char_i_1'')) \<and>
            is_valid_w8 s35' (Ptr (symbol_table ''echo_char_i_2'')) \<and>
            s35' = s34'\<rbrace>
     get_echo_char_i'
    \<lbrace>\<lambda>r36' s35'. r36' \<in> {Ptr (symbol_table
      ''echo_char_i_1''), Ptr (symbol_table ''echo_char_i_2'')} \<and>
      s35' = s34'\<rbrace>!" apply (rule allI) apply (simp add:get_echo_char_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>s34'. \<lbrace>\<lambda>s35'. globals_frame_intact s35' \<and> ipc_buffer_valid s35' \<and> tls_valid s35' \<and> thread_index_C (tls s35') \<in> {1..thread_count} \<and> is_valid_w8 s35' (PTR(8 word) (symbol_table ''echo_char_i_1'')) \<and> is_valid_w8 s35' (PTR(8 word) (symbol_table ''echo_char_i_2'')) \<and> s35' = s34'\<rbrace> get_echo_char_i' \<lbrace>\<lambda>r36' s35'. r36' \<in> {PTR(8 word) (symbol_table ''echo_char_i_1''), PTR(8 word) (symbol_table ''echo_char_i_2'')} \<and> s35' = s34'\<rbrace>! proof (prove)
goal (1 subgoal):
 1. \<And>s34'. \<lbrace>\<lambda>s35'. globals_frame_intact s35' \<and> ipc_buffer_valid s35' \<and> tls_valid s35' \<and> thread_index_C (tls s35') \<in> {1..thread_count} \<and> is_valid_w8 s35' (PTR(8 word) (symbol_table ''echo_char_i_1'')) \<and> is_valid_w8 s35' (PTR(8 word) (symbol_table ''echo_char_i_2'')) \<and> s35' = s34'\<rbrace> get_echo_char_i' \<lbrace>\<lambda>r36' s35'. r36' \<in> {PTR(8 word) (symbol_table ''echo_char_i_1''), PTR(8 word) (symbol_table ''echo_char_i_2'')} \<and> s35' = s34'\<rbrace>! proof (prove)
goal (1 subgoal):
 1. \<And>s34'. \<lbrace>\<lambda>s35'. globals_frame_intact s35' \<and> ipc_buffer_valid s35' \<and> tls_valid s35' \<and> 1 \<le> thread_index_C (tls s35') \<and> thread_index_C (tls s35') \<le> thread_count \<and> is_valid_w8 s35' (PTR(8 word) (symbol_table ''echo_char_i_1'')) \<and> is_valid_w8 s35' (PTR(8 word) (symbol_table ''echo_char_i_2'')) \<and> s35' = s34'\<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_w8 s (PTR(8 word) (symbol_table ''echo_char_i_1'')));
return (PTR(8 word) (symbol_table ''echo_char_i_1''))
od)
  condition (\<lambda>s. thread_index_C (heap_camkes_tls_t_C s ret') = 2)
  (do y <- guard (\<lambda>s. is_valid_w8 s (PTR(8 word) (symbol_table ''echo_char_i_2'')));
return (PTR(8 word) (symbol_table ''echo_char_i_2''))
od)
  (do y <- abort';
fail
od)
od \<lbrace>\<lambda>r36' s35'. (r36' = PTR(8 word) (symbol_table ''echo_char_i_1'') \<or> r36' = PTR(8 word) (symbol_table ''echo_char_i_2'')) \<and> s35' = s34'\<rbrace>! proof (prove)
goal (1 subgoal):
 1. \<And>s34' 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_w8 s (PTR(8 word) (symbol_table ''echo_char_i_1'')) \<and> is_valid_w8 s (PTR(8 word) (symbol_table ''echo_char_i_2'')) \<and> s = s34' \<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(8 word) (symbol_table ''echo_char_i_1'') = PTR(8 word) (symbol_table ''echo_char_i_1'') \<or> PTR(8 word) (symbol_table ''echo_char_i_1'') = PTR(8 word) (symbol_table ''echo_char_i_2'')) \<and> s = s34') \<and> is_valid_w8 s (PTR(8 word) (symbol_table ''echo_char_i_1'')) else if thread_index_C (heap_camkes_tls_t_C s (tls_ptr s)) = 2 then ((PTR(8 word) (symbol_table ''echo_char_i_2'') = PTR(8 word) (symbol_table ''echo_char_i_1'') \<or> PTR(8 word) (symbol_table ''echo_char_i_2'') = PTR(8 word) (symbol_table ''echo_char_i_2'')) \<and> s = s34') \<and> is_valid_w8 s (PTR(8 word) (symbol_table ''echo_char_i_2'')) else False) \<and> is_valid_camkes_tls_t_C s (tls_ptr s) proof (prove)
goal (1 subgoal):
 1. \<And>s34'. \<lbrakk>globals_frame_intact s34'; ipc_buffer_valid s34'; is_valid_camkes_tls_t_C s34' (tls_ptr s34'); 1 \<le> thread_index_C (heap_camkes_tls_t_C s34' (tls_ptr s34')); thread_index_C (heap_camkes_tls_t_C s34' (tls_ptr s34')) \<le> 2; is_valid_w8 s34' (PTR(8 word) (symbol_table ''echo_char_i_1'')); is_valid_w8 s34' (PTR(8 word) (symbol_table ''echo_char_i_2'')); thread_index_C (heap_camkes_tls_t_C s34' (tls_ptr s34')) \<noteq> 2\<rbrakk> \<Longrightarrow> thread_index_C (heap_camkes_tls_t_C s34' (tls_ptr s34')) = 1 proof (prove)
goal:
No subgoals!