From de0467013b4c29f630066c9052c56afa89ebc75b Mon Sep 17 00:00:00 2001
From: Adam Megacz
Date: Sun, 24 Apr 2011 00:04:13 -0700
Subject: [PATCH] NaturalDeduction: add nd_swap, nd_prod_split, and some
tactics
---
src/NaturalDeduction.v | 38 ++++++++++++++++++++++++++++++++++++++
1 file changed, 38 insertions(+)
diff --git a/src/NaturalDeduction.v b/src/NaturalDeduction.v
index 56d74cd..4ecc166 100644
--- a/src/NaturalDeduction.v
+++ b/src/NaturalDeduction.v
@@ -589,6 +589,44 @@ Section ND_Relation_Facts.
intros; apply (ndr_builtfrom_structural f); auto.
Defined.
+ Ltac nd_prod_preserves_comp_ltac P EQV :=
+ match goal with
+ [ |- context [ (?A ** ?B) ;; (?C ** ?D) ] ] =>
+ set (@ndr_prod_preserves_comp _ _ EQV _ _ A _ _ B _ C _ D) as P
+ end.
+
+ Lemma nd_swap A B C D (f:ND _ A B) (g:ND _ C D) :
+ (f ** nd_id C) ;; (nd_id B ** g) ===
+ (nd_id A ** g) ;; (f ** nd_id D).
+ setoid_rewrite <- ndr_prod_preserves_comp.
+ setoid_rewrite ndr_comp_left_identity.
+ setoid_rewrite ndr_comp_right_identity.
+ reflexivity.
+ Qed.
+
+ (* this tactical searches the environment; setoid_rewrite doesn't seem to be able to do that properly sometimes *)
+ Ltac nd_swap_ltac P EQV :=
+ match goal with
+ [ |- context [ (?F ** nd_id _) ;; (nd_id _ ** ?G) ] ] =>
+ set (@nd_swap _ _ EQV _ _ _ _ F G) as P
+ end.
+
+ Lemma nd_prod_split_left A B C D (f:ND _ A B) (g:ND _ B C) :
+ nd_id D ** (f ;; g) ===
+ (nd_id D ** f) ;; (nd_id D ** g).
+ setoid_rewrite <- ndr_prod_preserves_comp.
+ setoid_rewrite ndr_comp_left_identity.
+ reflexivity.
+ Qed.
+
+ Lemma nd_prod_split_right A B C D (f:ND _ A B) (g:ND _ B C) :
+ (f ;; g) ** nd_id D ===
+ (f ** nd_id D) ;; (g ** nd_id D).
+ setoid_rewrite <- ndr_prod_preserves_comp.
+ setoid_rewrite ndr_comp_left_identity.
+ reflexivity.
+ Qed.
+
End ND_Relation_Facts.
(* a generalization of the procedure used to build (nd_id n) from nd_id0 and nd_id1 *)
--
1.7.10.4