123 lines
4.0 KiB
Plaintext
123 lines
4.0 KiB
Plaintext
(*
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* Copyright 2020, Data61, CSIRO (ABN 41 687 119 230)
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*
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* SPDX-License-Identifier: BSD-2-Clause
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*)
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theory Word_Lemmas_32_Internal
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imports Word_Lib_Sumo Machine_Word_32
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begin
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lemmas sint_eq_uint_32 = sint_eq_uint_2pl[where 'a=32, simplified]
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lemmas sle_positive_32 = sle_le_2pl[where 'a=32, simplified]
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lemmas sless_positive_32 = sless_less_2pl[where 'a=32, simplified]
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lemma zero_le_sint_32:
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"\<lbrakk> 0 \<le> (a :: word32); a < 0x80000000 \<rbrakk>
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\<Longrightarrow> 0 \<le> sint a"
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by (clarsimp simp: sint_eq_uint_32 unat_less_helper)
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lemmas unat_add_simple = iffD1[OF unat_add_lem[where 'a = 32, folded word_bits_def]]
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lemma upto_enum_inc_1:
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"a < 2 ^ word_bits - 1
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\<Longrightarrow> [(0:: 'a :: len word) .e. 1 + a] = [0.e.a] @ [(1+a)]"
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using upper_trivial upto_enum_inc_1_len by force
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lemmas upt_enum_offset_trivial =
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upt_enum_offset_trivial[where 'a=32, folded word_bits_def]
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lemmas unat32_eq_of_nat = unat_eq_of_nat[where 'a=32, folded word_bits_def]
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declare mask_32_max_word[simp]
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lemma le_32_mask_eq:
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"(bits :: word32) \<le> 32 \<Longrightarrow> bits && mask 6 = bits"
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by (fastforce elim: le_less_trans intro: less_mask_eq)
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lemmas scast_1_32[simp] = scast_1[where 'a=32]
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lemmas mask_32_id[simp] = mask_len_id[where 'a=32, folded word_bits_def]
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lemmas t2p_shiftr_32 = t2p_shiftr[where 'a=32, folded word_bits_def]
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lemma mask_eq1_nochoice:
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"(x :: word32) && 1 = x
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\<Longrightarrow> x = 0 \<or> x = 1"
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using mask_eq1_nochoice len32 by force
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lemmas const_le_unat_word_32 = const_le_unat[where 'a=32, folded word_bits_def]
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lemmas createNewCaps_guard_helper =
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createNewCaps_guard[where 'a=32, folded word_bits_def]
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lemma word_log2_max_word32[simp]:
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"word_log2 (w :: 32 word) < 32"
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using word_log2_max[where w=w]
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by (simp add: word_size)
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(* FIXME: specialize using pow_sub_less_word *)
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lemma mapping_two_power_16_64_inequality:
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assumes sz: "sz \<le> 4" and len: "unat (len :: word32) = 2 ^ sz"
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shows "unat (len * 8 - 1) \<le> 127"
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using pow_sub_less[where 'a=32 and b=3, simplified]
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proof -
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have len2: "len = 2 ^ sz"
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apply (rule word_unat.Rep_eqD, simp only: len)
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using sz
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apply simp
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done
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show ?thesis using two_power_increasing_less_1[where 'a=32 and n="sz + 3" and m=7]
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by (simp add: word_le_nat_alt sz power_add len2 field_simps bintrunc_Suc_numeral)
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qed
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lemmas pre_helper2_32 = pre_helper2[where 'a=32, folded word_bits_def]
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lemmas of_nat_shift_distinct_helper_machine =
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of_nat_shift_distinct_helper[where 'a=32, folded word_bits_def]
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lemmas ptr_add_distinct_helper_32 =
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ptr_add_distinct_helper[where 'a=32, folded word_bits_def]
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lemmas mask_out_eq_0_32 = mask_out_eq_0[where 'a=32, folded word_bits_def]
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lemmas neg_mask_mask_unat_32 = neg_mask_mask_unat[where 'a=32, folded word_bits_def]
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lemmas unat_less_iff_32 = unat_less_iff[where 'a=32, folded word_bits_def]
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lemmas is_aligned_no_overflow3_32 = is_aligned_no_overflow3[where 'a=32, folded word_bits_def]
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lemmas unat_ucast_16_32 = unat_signed_ucast_less_ucast[where 'a=16 and 'b=32, simplified]
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(* FIXME: generalize? *)
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lemma scast_mask_8:
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"scast (mask 8 :: sword32) = (mask 8 :: word32)"
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by (clarsimp simp: mask_eq)
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lemmas ucast_le_8_32_equiv = ucast_le_up_down_iff[where 'a=8 and 'b=32, simplified]
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lemma signed_unat_minus_one_32:
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"unat (-1 :: 32 signed word) = 4294967295"
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by (simp del: word_pow_0 diff_0 add: unat_sub_if' minus_one_word)
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lemmas two_bits_cases_32 = two_bits_cases[where 'a=32, simplified]
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lemmas word_ctz_not_minus_1_32 = word_ctz_not_minus_1[where 'a=32, simplified]
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lemmas sint_ctz_32 = sint_ctz[where 'a=32, simplified]
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(* FIXME: inline these? *)
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lemmas scast_specific_plus32 =
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scast_of_nat_signed_to_unsigned_add[where 'a=32 and x="word_ctz x" and y="0x20" for x,
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simplified]
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lemmas scast_specific_plus32_signed =
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scast_of_nat_unsigned_to_signed_add[where 'a=32 and x="word_ctz x" and y="0x20" for x,
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simplified]
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lemma neq_0_unat: "x \<noteq> 0 \<Longrightarrow> 0 < unat x" for x::machine_word
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by (simp add: unat_gt_0)
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end |