83 lines
2.6 KiB
Plaintext
83 lines
2.6 KiB
Plaintext
(*
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* Copyright 2014, 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 ArchLevityCatch_AI
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imports
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"ArchBCorres_AI"
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"Lib.LemmaBucket"
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"Lib.SplitRule"
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begin
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context Arch begin global_naming X64
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lemma asid_high_bits_of_shift :
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"asid_high_bits_of (ucast x << asid_low_bits) = x"
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apply (simp add: asid_high_bits_of_def)
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apply (rule word_eqI)
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apply (simp add: word_size nth_ucast nth_shiftr nth_shiftl asid_low_bits_def)
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done
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lemma ptrFormPAddr_addFromPPtr :
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"ptrFromPAddr (Platform.X64.addrFromPPtr x) = x"
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by (simp add: ptrFromPAddr_def Platform.X64.addrFromPPtr_def)
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(****** From GeneralLib *******)
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lemma asid_high_bits_of_add_ucast:
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"is_aligned w asid_low_bits \<Longrightarrow>
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asid_high_bits_of (ucast (x::9 word) + w) = asid_high_bits_of w"
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apply (rule word_eqI)
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apply (simp add: word_size asid_high_bits_of_def nth_ucast nth_shiftr is_aligned_nth)
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apply (subst word_plus_and_or_coroll)
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apply (rule word_eqI)
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apply (clarsimp simp: nth_ucast)
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apply (drule test_bit_size)
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apply (simp add: word_size asid_low_bits_def)
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apply (auto dest: test_bit_size simp: word_size asid_low_bits_def nth_ucast)
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done
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lemma asid_high_bits_of_add:
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"\<lbrakk>is_aligned w asid_low_bits; x \<le> 2 ^ asid_low_bits - 1\<rbrakk>
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\<Longrightarrow> asid_high_bits_of (w + x) = asid_high_bits_of w"
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apply (rule word_eqI)
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apply (simp add: word_size asid_high_bits_of_def nth_ucast nth_shiftr
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is_aligned_nth)
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apply (drule le2p_bits_unset, simp add: asid_low_bits_def word_bits_def)
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apply (subst word_plus_and_or_coroll)
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apply (rule word_eqI)
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apply (clarsimp simp: word_size)
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apply (case_tac "na < asid_low_bits")
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apply (simp add: asid_low_bits_def linorder_not_less word_bits_def)
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apply (auto dest: test_bit_size
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simp: asid_low_bits_def nth_ucast)
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done
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lemma pageBits_less_word_bits [simp]:
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"pageBits < word_bits" by (simp add: pageBits_def word_bits_conv)
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lemma mask_out_8_le_kernel_base:
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"(x && ~~ mask 8 \<ge> kernel_base >> 20) = (x \<ge> kernel_base >> 20)"
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apply (rule iffI)
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apply (erule order_trans, rule word_and_le2)
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apply (drule_tac n=8 in neg_mask_mono_le)
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apply (simp add: kernel_base_def mask_def)
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done
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lemma mask_out_8_less_kernel_base:
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"(x && ~~ mask 8 < kernel_base >> 20) = (x < kernel_base >> 20)"
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using mask_out_8_le_kernel_base[where x=x]
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by (simp add: linorder_not_less[symmetric])
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lemma aobj_ref_arch_cap[simp]:
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"aobj_ref (arch_default_cap aty ptr us dev) = Some ptr"
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apply (case_tac aty)
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apply (simp_all add: aobj_ref_def arch_default_cap_def p_assoc_help)
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done
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end
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end
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