theory SR_lemmas_C

lemma cap_get_tag_ReplyCap:
  assumes cr: "ccap_relation cap cap'"
  shows "(cap_get_tag cap' = scast cap_reply_cap) =
  (cap =
      ReplyCap (ctcb_ptr_to_tcb_ptr (Ptr (cap_reply_cap_CL.capTCBPtr_CL (cap_reply_cap_lift cap'))))
               (to_bool (capReplyMaster_CL (cap_reply_cap_lift cap')))
               (to_bool (capReplyCanGrant_CL (cap_reply_cap_lift cap'))))" using cr apply - apply (rule iffI) apply (erule ccap_relationE) apply (clarsimp simp add: cap_lifts cap_to_H_def) apply (simp add: cap_get_tag_isCap isCap_simps) done

(* Proof state trace *)
proof (prove)
goal (1 subgoal):
 1. (cap_get_tag cap' = SCAST(32 signed \<rightarrow> 32) cap_reply_cap) = (cap = capability.ReplyCap (ctcb_ptr_to_tcb_ptr (tcb_Ptr (cap_reply_cap_CL.capTCBPtr_CL (cap_reply_cap_lift cap')))) (to_bool (capReplyMaster_CL (cap_reply_cap_lift cap'))) (to_bool (capReplyCanGrant_CL (cap_reply_cap_lift cap')))) proof (prove)
using this:
ccap_relation cap cap'

goal (1 subgoal):
 1. (cap_get_tag cap' = SCAST(32 signed \<rightarrow> 32) cap_reply_cap) = (cap = capability.ReplyCap (ctcb_ptr_to_tcb_ptr (tcb_Ptr (cap_reply_cap_CL.capTCBPtr_CL (cap_reply_cap_lift cap')))) (to_bool (capReplyMaster_CL (cap_reply_cap_lift cap'))) (to_bool (capReplyCanGrant_CL (cap_reply_cap_lift cap')))) proof (prove)
goal (1 subgoal):
 1. ccap_relation cap cap' \<Longrightarrow> (cap_get_tag cap' = SCAST(32 signed \<rightarrow> 32) cap_reply_cap) = (cap = capability.ReplyCap (ctcb_ptr_to_tcb_ptr (tcb_Ptr (cap_reply_cap_CL.capTCBPtr_CL (cap_reply_cap_lift cap')))) (to_bool (capReplyMaster_CL (cap_reply_cap_lift cap'))) (to_bool (capReplyCanGrant_CL (cap_reply_cap_lift cap')))) proof (prove)
goal (2 subgoals):
 1. \<lbrakk>ccap_relation cap cap'; cap_get_tag cap' = SCAST(32 signed \<rightarrow> 32) cap_reply_cap\<rbrakk> \<Longrightarrow> cap = capability.ReplyCap (ctcb_ptr_to_tcb_ptr (tcb_Ptr (cap_reply_cap_CL.capTCBPtr_CL (cap_reply_cap_lift cap')))) (to_bool (capReplyMaster_CL (cap_reply_cap_lift cap'))) (to_bool (capReplyCanGrant_CL (cap_reply_cap_lift cap')))
 2. \<lbrakk>ccap_relation cap cap'; cap = capability.ReplyCap (ctcb_ptr_to_tcb_ptr (tcb_Ptr (cap_reply_cap_CL.capTCBPtr_CL (cap_reply_cap_lift cap')))) (to_bool (capReplyMaster_CL (cap_reply_cap_lift cap'))) (to_bool (capReplyCanGrant_CL (cap_reply_cap_lift cap')))\<rbrakk> \<Longrightarrow> cap_get_tag cap' = SCAST(32 signed \<rightarrow> 32) cap_reply_cap proof (prove)
goal (2 subgoals):
 1. \<And>vl. \<lbrakk>cap_get_tag cap' = SCAST(32 signed \<rightarrow> 32) cap_reply_cap; cap_lift cap' = Some vl; cap = cap_to_H vl; c_valid_cap cap'\<rbrakk> \<Longrightarrow> cap = capability.ReplyCap (ctcb_ptr_to_tcb_ptr (tcb_Ptr (cap_reply_cap_CL.capTCBPtr_CL (cap_reply_cap_lift cap')))) (to_bool (capReplyMaster_CL (cap_reply_cap_lift cap'))) (to_bool (capReplyCanGrant_CL (cap_reply_cap_lift cap')))
 2. \<lbrakk>ccap_relation cap cap'; cap = capability.ReplyCap (ctcb_ptr_to_tcb_ptr (tcb_Ptr (cap_reply_cap_CL.capTCBPtr_CL (cap_reply_cap_lift cap')))) (to_bool (capReplyMaster_CL (cap_reply_cap_lift cap'))) (to_bool (capReplyCanGrant_CL (cap_reply_cap_lift cap')))\<rbrakk> \<Longrightarrow> cap_get_tag cap' = SCAST(32 signed \<rightarrow> 32) cap_reply_cap proof (prove)
goal (1 subgoal):
 1. \<lbrakk>ccap_relation cap cap'; cap = capability.ReplyCap (ctcb_ptr_to_tcb_ptr (tcb_Ptr (cap_reply_cap_CL.capTCBPtr_CL (cap_reply_cap_lift cap')))) (to_bool (capReplyMaster_CL (cap_reply_cap_lift cap'))) (to_bool (capReplyCanGrant_CL (cap_reply_cap_lift cap')))\<rbrakk> \<Longrightarrow> cap_get_tag cap' = SCAST(32 signed \<rightarrow> 32) cap_reply_cap proof (prove)
goal:
No subgoals!