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lib: add some word lemmas about sless, word_bits

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Michael Sproul 2018-05-07 16:32:09 +10:00 committed by Joel Beeren
parent e5ecf10b14
commit df9c791a3f
2 changed files with 11 additions and 0 deletions
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5
lib/Word_Lib/Word_Lemmas.thy
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@ -3769,6 +3769,11 @@ lemma zero_sle_ucast_up:
apply arith
done
lemma word_le_ucast_sless:
"\<lbrakk> x \<le> y; y \<noteq> -1; LENGTH('a) < LENGTH('b) \<rbrakk> \<Longrightarrow>
UCAST (('a :: len) \<rightarrow> ('b :: len) signed) x <s ucast (y + 1)"
by (clarsimp simp: word_le_make_less word_sless_alt sint_ucast_eq_uint is_down word_less_def)
lemma msb_ucast_eq:
"len_of TYPE('a) = len_of TYPE('b) \<Longrightarrow>
msb (ucast x :: ('a::len) word) = msb (x :: ('b::len) word)"

6
lib/Word_Lib/Word_Lemmas_64.thy
View File

@ -84,6 +84,12 @@ lemma unat_less_word_bits:
lemmas unat_mask_word64' = unat_mask[where 'a=64]
lemmas unat_mask_word64 = unat_mask_word64'[folded word_bits_def]
lemma unat_less_2p_word_bits:
"unat (x :: 64 word) < 2 ^ word_bits"
apply (simp only: word_bits_def)
apply (rule unat_lt2p)
done
lemma Suc_unat_mask_div:
"Suc (unat (mask sz div word_size::word64)) = 2 ^ (min sz word_bits - 3)"
apply (case_tac "sz < word_bits")