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lib: move some lemmas from bitfield proofs to word-lib

This commit is contained in:
Matthew Brecknell 2017-08-10 17:30:37 +10:00
parent caeab8889a
commit 27ae2ca752
2 changed files with 17 additions and 17 deletions
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17
lib/BitFieldProofsLib.thy
View File

@ -14,23 +14,6 @@ imports
TypHeapLib
begin
(* FIXME: should probably move to Word_Lib *)
definition
sign_extend :: "nat \<Rightarrow> 'a::len word \<Rightarrow> 'a word"
where
"sign_extend n w \<equiv> if w!!n then w || ~~mask n else w"
lemma sign_extend_def':
"sign_extend n w = (if w!!n then w || ~~mask (Suc n) else w)"
apply (rule word_eqI)
apply (auto dest: less_antisym simp: sign_extend_def word_size word_ops_nth_size)
done
(* FIXME: move to Word_Lib *)
lemma nth_is_and_neq_0:
"(x::'a::len word) !! n = (x && 2 ^ n \<noteq> 0)"
by (subst and_neq_0_is_nth; rule refl)
lemmas guard_simps =
word_sle_def word_sless_def scast_id

17
lib/Word_Lib/Word_Lemmas.thy
View File

@ -2816,6 +2816,10 @@ lemma and_eq_0_is_nth:
lemmas arg_cong_Not = arg_cong [where f=Not]
lemmas and_neq_0_is_nth = arg_cong_Not [OF and_eq_0_is_nth, simplified]
lemma nth_is_and_neq_0:
"(x::'a::len word) !! n = (x && 2 ^ n \<noteq> 0)"
by (subst and_neq_0_is_nth; rule refl)
lemma mask_Suc_0 : "mask (Suc 0) = 1"
by (simp add: mask_def)
@ -5520,4 +5524,17 @@ lemma word_of_nat_inj:
by (rule contrapos_pp[OF of_nats]; cases "x < y"; cases "y < x")
(auto dest: bounded[THEN of_nat_mono_maybe])
(* Sign-extend from bit n *)
definition
sign_extend :: "nat \<Rightarrow> 'a::len word \<Rightarrow> 'a word"
where
"sign_extend n w \<equiv> if w!!n then w || ~~mask n else w"
lemma sign_extend_def':
"sign_extend n w = (if w!!n then w || ~~mask (Suc n) else w)"
apply (rule word_eqI)
apply (auto dest: less_antisym simp: sign_extend_def word_size word_ops_nth_size)
done
end