isabelle2021-1 word_lib: add lemmas from l4v

Signed-off-by: Gerwin Klein <gerwin.klein@proofcraft.systems>

lib/Word_Lib/Machine_Word_32.thy

@@ -122,8 +122,9 @@ lemma word_ge_min:
   \<open>- (2 ^ (word_bits - 1)) \<le> sint x\<close> for x :: machine_word
   using sint_ge [of x] by (simp add: word_bits_def)
 
+(* We want the rhs unfolded here for later matching *)
 lemma word_rsplit_0:
-  "word_rsplit (0 :: machine_word) = replicate (word_bits div 8) (0 :: 8 word)"
+  "word_rsplit (0::machine_word) = [0, 0, 0, (0::8 word)]"
   by (simp add: word_rsplit_def bin_rsplit_def word_bits_def word_size_def Cons_replicate_eq)
 
 lemma x_less_2_0_1:

lib/Word_Lib/Machine_Word_64.thy

@@ -122,8 +122,9 @@ lemma word_ge_min:
   \<open>- (2 ^ (word_bits - 1)) \<le> sint x\<close> for x :: machine_word
   using sint_ge [of x] by (simp add: word_bits_def)
 
+(* We want the rhs unfolded here for later matching *)
 lemma word_rsplit_0:
-  "word_rsplit (0 :: machine_word) = replicate (word_bits div 8) (0 :: 8 word)"
+  "word_rsplit (0::machine_word) = [0, 0, 0, 0, 0, 0, 0, (0::8 word)]"
   by (simp add: word_rsplit_def bin_rsplit_def word_bits_def word_size_def Cons_replicate_eq)
 
 lemma x_less_2_0_1:

lib/Word_Lib/More_Word_Operations.thy

@@ -783,6 +783,10 @@ lemma from_bool_eqI:
   unfolding from_bool_def
   by (auto split: bool.splits)
 
+lemma from_bool_odd_eq_and:
+  "from_bool (odd w) = w AND 1"
+  unfolding from_bool_def by (simp add: word_and_1)
+
 lemma neg_mask_in_mask_range:
   "is_aligned ptr bits \<Longrightarrow> (ptr' AND NOT(mask bits) = ptr) = (ptr' \<in> mask_range ptr bits)"
   apply (erule is_aligned_get_word_bits)

lib/Word_Lib/Word_Lemmas.thy

@@ -19,6 +19,8 @@ theory Word_Lemmas
     Word_EqI
 begin
 
+lemmas take_bit_Suc_numeral[simp] = take_bit_Suc[where a="numeral w" for w]
+
 context
   includes bit_operations_syntax
 begin
@@ -1886,6 +1888,28 @@ lemma nasty_split_less:
    apply simp+
   done
 
+lemma is_aligned_shiftr_add:
+ "\<lbrakk>is_aligned a n; is_aligned b m; b < 2^n; m \<le> n; n < LENGTH('a)\<rbrakk>
+  \<Longrightarrow> a + b >> m = (a >> m) + (b >> m)" for a :: "'a::len word"
+  apply(simp add: shiftr_div_2n_w word_size)
+  apply (rule word_unat_eq_iff[THEN iffD2])
+  apply (subst unat_plus_simple[THEN iffD1])
+   apply (subst shiftr_div_2n_w[symmetric])+
+   apply (rule is_aligned_no_wrap')
+    apply (rule is_aligned_shiftr[where n = "n - m"])
+    apply simp
+   apply (rule shiftr_less_t2n)
+   apply simp
+  apply (simp add:unat_div)
+  apply (subst unat_plus_simple[THEN iffD1])
+   apply (erule is_aligned_no_wrap')
+   apply simp
+  by (meson div_plus_div_distrib_dvd_left is_aligned_iff_dvd_nat is_aligned_weaken)
+
+lemma shiftr_eq_neg_mask_eq:
+  "a >> b = c >> b \<Longrightarrow> a AND NOT (mask b) = c AND NOT (mask b)" for a :: "'a::len word"
+  by word_eqI (metis less_eqE)
+
 end
 
 end