60 lines
2.4 KiB
Plaintext
60 lines
2.4 KiB
Plaintext
(*
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* Copyright 2018, General Dynamics C4 Systems
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*
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* SPDX-License-Identifier: GPL-2.0-only
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*)
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theory Rights_AI
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imports "ASpec.VMRights_A"
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begin
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lemma validate_vm_rights_idem[simp]:
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"validate_vm_rights (validate_vm_rights rights) = validate_vm_rights rights"
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by (clarsimp simp: validate_vm_rights_def vm_kernel_only_def vm_read_only_def vm_read_write_def)
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lemma validate_vm_rights_inter_rw:
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"validate_vm_rights (vm_read_write \<inter> rights) = validate_vm_rights rights"
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apply (rule set_eqI)
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apply (clarsimp simp: validate_vm_rights_def vm_read_write_def)
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done
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lemma valid_validate_vm_rights[simp]:
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"validate_vm_rights rs \<in> valid_vm_rights"
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and validate_vm_rights_subseteq[simp]:
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"validate_vm_rights rs \<subseteq> rs"
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and validate_vm_rights_simps[simp]:
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"validate_vm_rights vm_read_write = vm_read_write"
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"validate_vm_rights vm_read_only = vm_read_only"
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"validate_vm_rights vm_kernel_only = vm_kernel_only"
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by (simp_all add: validate_vm_rights_def valid_vm_rights_def
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vm_read_write_def vm_read_only_def vm_kernel_only_def)
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lemma validate_vm_rights_inter:
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"validate_vm_rights (validate_vm_rights fun \<inter> msk) =
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validate_vm_rights (fun \<inter> msk)"
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by (simp add: validate_vm_rights_def vm_read_write_def vm_read_only_def
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vm_kernel_only_def)
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lemma validate_vm_rights_eq[simp]:
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"rs \<in> valid_vm_rights \<Longrightarrow> validate_vm_rights rs = rs"
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by (auto simp add: validate_vm_rights_def valid_vm_rights_def
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vm_read_write_def vm_read_only_def vm_kernel_only_def)
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lemma validate_vm_rights_def':
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"validate_vm_rights rs =
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(THE rs'. rs' \<subseteq> rs \<and> rs' : valid_vm_rights \<and>
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(\<forall>rs''. rs'' \<subseteq> rs \<longrightarrow> rs'' : valid_vm_rights \<longrightarrow> rs'' \<subseteq> rs'))"
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apply (rule the_equality[symmetric])
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apply (auto simp add: validate_vm_rights_def valid_vm_rights_def
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vm_read_write_def vm_read_only_def vm_kernel_only_def)[1]
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apply (simp add: validate_vm_rights_def valid_vm_rights_def
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vm_read_write_def vm_read_only_def vm_kernel_only_def)
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apply safe
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apply simp+
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apply (drule_tac x="{AllowRead, AllowWrite}" in spec, simp+)
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apply (drule_tac x="{AllowRead, AllowWrite}" in spec, simp+)
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apply (drule_tac x="{AllowRead, AllowWrite}" in spec, simp+)
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apply (drule_tac x="{AllowRead}" in spec, simp)
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done
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end |