theory SR_lemmas_C

lemma cap_get_tag_UntypedCap:
  assumes cr: "ccap_relation cap cap'"
  shows "(cap_get_tag cap' = scast cap_untyped_cap) =
  (cap = UntypedCap (to_bool (capIsDevice_CL (cap_untyped_cap_lift cap')))
                    (capPtr_CL (cap_untyped_cap_lift cap'))
                    (unat (capBlockSize_CL (cap_untyped_cap_lift cap')))
                    (unat (capFreeIndex_CL (cap_untyped_cap_lift cap') << 4)))" 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_untyped_cap) = (cap = capability.UntypedCap (to_bool (capIsDevice_CL (cap_untyped_cap_lift cap'))) (capPtr_CL (cap_untyped_cap_lift cap')) (unat (capBlockSize_CL (cap_untyped_cap_lift cap'))) (unat (capFreeIndex_CL (cap_untyped_cap_lift cap') << 4))) proof (prove)
using this:
ccap_relation cap cap'

goal (1 subgoal):
 1. (cap_get_tag cap' = SCAST(32 signed \<rightarrow> 32) cap_untyped_cap) = (cap = capability.UntypedCap (to_bool (capIsDevice_CL (cap_untyped_cap_lift cap'))) (capPtr_CL (cap_untyped_cap_lift cap')) (unat (capBlockSize_CL (cap_untyped_cap_lift cap'))) (unat (capFreeIndex_CL (cap_untyped_cap_lift cap') << 4))) proof (prove)
goal (1 subgoal):
 1. ccap_relation cap cap' \<Longrightarrow> (cap_get_tag cap' = SCAST(32 signed \<rightarrow> 32) cap_untyped_cap) = (cap = capability.UntypedCap (to_bool (capIsDevice_CL (cap_untyped_cap_lift cap'))) (capPtr_CL (cap_untyped_cap_lift cap')) (unat (capBlockSize_CL (cap_untyped_cap_lift cap'))) (unat (capFreeIndex_CL (cap_untyped_cap_lift cap') << 4))) proof (prove)
goal (2 subgoals):
 1. \<lbrakk>ccap_relation cap cap'; cap_get_tag cap' = SCAST(32 signed \<rightarrow> 32) cap_untyped_cap\<rbrakk> \<Longrightarrow> cap = capability.UntypedCap (to_bool (capIsDevice_CL (cap_untyped_cap_lift cap'))) (capPtr_CL (cap_untyped_cap_lift cap')) (unat (capBlockSize_CL (cap_untyped_cap_lift cap'))) (unat (capFreeIndex_CL (cap_untyped_cap_lift cap') << 4))
 2. \<lbrakk>ccap_relation cap cap'; cap = capability.UntypedCap (to_bool (capIsDevice_CL (cap_untyped_cap_lift cap'))) (capPtr_CL (cap_untyped_cap_lift cap')) (unat (capBlockSize_CL (cap_untyped_cap_lift cap'))) (unat (capFreeIndex_CL (cap_untyped_cap_lift cap') << 4))\<rbrakk> \<Longrightarrow> cap_get_tag cap' = SCAST(32 signed \<rightarrow> 32) cap_untyped_cap proof (prove)
goal (2 subgoals):
 1. \<And>vl. \<lbrakk>cap_get_tag cap' = SCAST(32 signed \<rightarrow> 32) cap_untyped_cap; cap_lift cap' = Some vl; cap = cap_to_H vl; c_valid_cap cap'\<rbrakk> \<Longrightarrow> cap = capability.UntypedCap (to_bool (capIsDevice_CL (cap_untyped_cap_lift cap'))) (capPtr_CL (cap_untyped_cap_lift cap')) (unat (capBlockSize_CL (cap_untyped_cap_lift cap'))) (unat (capFreeIndex_CL (cap_untyped_cap_lift cap') << 4))
 2. \<lbrakk>ccap_relation cap cap'; cap = capability.UntypedCap (to_bool (capIsDevice_CL (cap_untyped_cap_lift cap'))) (capPtr_CL (cap_untyped_cap_lift cap')) (unat (capBlockSize_CL (cap_untyped_cap_lift cap'))) (unat (capFreeIndex_CL (cap_untyped_cap_lift cap') << 4))\<rbrakk> \<Longrightarrow> cap_get_tag cap' = SCAST(32 signed \<rightarrow> 32) cap_untyped_cap proof (prove)
goal (1 subgoal):
 1. \<lbrakk>ccap_relation cap cap'; cap = capability.UntypedCap (to_bool (capIsDevice_CL (cap_untyped_cap_lift cap'))) (capPtr_CL (cap_untyped_cap_lift cap')) (unat (capBlockSize_CL (cap_untyped_cap_lift cap'))) (unat (capFreeIndex_CL (cap_untyped_cap_lift cap') << 4))\<rbrakk> \<Longrightarrow> cap_get_tag cap' = SCAST(32 signed \<rightarrow> 32) cap_untyped_cap proof (prove)
goal:
No subgoals!