From: Adam Megacz <megacz@cs.berkeley.edu>
Date: Fri, 25 Mar 2011 18:10:10 +0000 (-0700)
Subject: add n-ary form of nd_weak
X-Git-Url: http://git.megacz.com/?p=coq-hetmet.git;a=commitdiff_plain;h=fdebbea0c0303b8bba05779f2635c9a0e5c459b7

add n-ary form of nd_weak
---

diff --git a/src/NaturalDeduction.v b/src/NaturalDeduction.v
index cd225da..5cf67db 100644
--- a/src/NaturalDeduction.v
+++ b/src/NaturalDeduction.v
@@ -182,6 +182,13 @@ Section Natural_Deduction.
       | T_Branch a b     => nd_prod (nd_id a) (nd_id b)
     end.
 
+  Fixpoint nd_weak' (sl:Tree ??Judgment) : sl /⋯⋯/ [] :=
+    match sl as SL return SL /⋯⋯/ [] with
+      | T_Leaf None      => nd_id0
+      | T_Leaf (Some x)  => nd_weak x
+      | T_Branch a b     => nd_prod (nd_weak' a) (nd_weak' b) ;; nd_cancelr
+    end.
+
   Hint Constructors Structural.
   Lemma nd_id_structural : forall sl, Structural (nd_id sl).
     intros.
@@ -189,6 +196,16 @@ Section Natural_Deduction.
     destruct a; auto.
     Defined.
 
+  Lemma weak'_structural : forall a, Structural (nd_weak' a).
+    intros.
+    induction a.
+    destruct a; auto.
+    simpl.
+    auto.
+    simpl.
+    auto.
+    Qed.
+
   (* An equivalence relation on proofs which is sensitive only to the logical content of the proof -- insensitive to
    * structural variations  *)
   Class ND_Relation :=