From bd0b50455f864f9c6d554f49da2877548662e187 Mon Sep 17 00:00:00 2001 From: Jason Gross Date: Sat, 8 Apr 2017 12:20:03 -0400 Subject: Add wordToZ_ZToWord_mod --- src/Util/FixedWordSizesEquality.v | 17 +++++++++++++++++ 1 file changed, 17 insertions(+) (limited to 'src/Util/FixedWordSizesEquality.v') diff --git a/src/Util/FixedWordSizesEquality.v b/src/Util/FixedWordSizesEquality.v index c8f37c86b..2371eda1a 100644 --- a/src/Util/FixedWordSizesEquality.v +++ b/src/Util/FixedWordSizesEquality.v @@ -120,6 +120,16 @@ Proof. assumption. Qed. +Lemma wordToZ_gen_ZToWord_gen_mod : forall {sz} w, (0 <= w)%Z -> wordToZ_gen (@ZToWord_gen sz w) = (w mod (2^Z.of_nat sz))%Z. +Proof. + unfold ZToWord_gen, wordToZ_gen. + intros. + rewrite wordToN_NToWord_mod. + rewrite N2Z.inj_mod by (destruct sz; simpl; congruence). + rewrite Z2N.id, N2Z.inj_pow, nat_N_Z by assumption. + reflexivity. +Qed. + Lemma ZToWord_gen_wordToZ_gen_ZToWord_gen : forall {sz1 sz2} v, (sz2 <= sz1)%nat -> @ZToWord_gen sz2 (wordToZ_gen (@ZToWord_gen sz1 v)) = ZToWord_gen v. Proof. @@ -162,6 +172,13 @@ Proof. assumption. Qed. +Lemma wordToZ_ZToWord_mod : forall {sz} v, (0 <= v)%Z -> wordToZ (@ZToWord sz v) = (v mod (2^Z.of_nat (2^sz)))%Z. +Proof. + unfold wordToZ, ZToWord, word_case_dep. + intros; break_match; apply wordToZ_gen_ZToWord_gen_mod; + assumption. +Qed. + Local Ltac handle_le := repeat match goal with | [ |- (S ?a <= 2^?b)%nat ] -- cgit v1.2.3