From 60bd3785db01f5275aaab52a2a5fec66caa9de53 Mon Sep 17 00:00:00 2001
From: Jason Gross <jgross@mit.edu>
Date: Mon, 7 Nov 2016 17:05:09 -0500
Subject: Add push_lift_option

---
 src/Util/Tuple.v | 24 ++++++++++++++++++++++++
 1 file changed, 24 insertions(+)

(limited to 'src/Util/Tuple.v')

diff --git a/src/Util/Tuple.v b/src/Util/Tuple.v
index c030a03f8..124ee1bf1 100644
--- a/src/Util/Tuple.v
+++ b/src/Util/Tuple.v
@@ -1,6 +1,9 @@
 Require Import Coq.Classes.Morphisms.
 Require Import Coq.Relations.Relation_Definitions.
 Require Import Coq.Lists.List.
+Require Import Crypto.Util.Option.
+Require Import Crypto.Util.Prod.
+Require Import Crypto.Util.Tactics.
 Require Import Crypto.Util.Decidable.
 Require Import Crypto.Util.ListUtil.
 Require Export Crypto.Util.FixCoqMistakes.
@@ -236,6 +239,27 @@ Proof.
   destruct xs as [ [? ?] | ]; reflexivity.
 Qed.
 
+Lemma push_lift_option {n A} {xs : tuple (option A) (S n)} {v}
+  : lift_option xs = Some v <-> xs = push_option (Some v).
+Proof.
+  simpl in *.
+  induction n; [ reflexivity | ].
+  specialize (IHn (fst xs) (fst v)).
+  repeat first [ progress destruct_head_hnf' prod
+               | progress destruct_head_hnf' and
+               | progress destruct_head_hnf' iff
+               | progress destruct_head_hnf' option
+               | progress inversion_option
+               | progress inversion_prod
+               | progress subst
+               | progress break_match
+               | progress simpl in *
+               | progress specialize_by exact eq_refl
+               | reflexivity
+               | apply conj
+               | intro ].
+Qed.
+
 Fixpoint fieldwise' {A B} (n:nat) (R:A->B->Prop) (a:tuple' A n) (b:tuple' B n) {struct n} : Prop.
   destruct n; simpl @tuple' in *.
   { exact (R a b). }
-- 
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