From 1a1f3c08b10e2cfbae42e73d7186caa9d90e0491 Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Tue, 27 Jun 2006 09:39:56 +0000
Subject: [PATCH] patched

---
 .../RELATIONAL-ARITHMETICS/add_gen.ma         | 26 ++++++++++++++++++-
 .../RELATIONAL-ARITHMETICS/add_props.ma       | 20 --------------
 .../{nat_gen.ma => nat_fwd.ma}                |  0
 3 files changed, 25 insertions(+), 21 deletions(-)
 rename matita/contribs/RELATIONAL-ARITHMETICS/{nat_gen.ma => nat_fwd.ma} (100%)

diff --git a/matita/contribs/RELATIONAL-ARITHMETICS/add_gen.ma b/matita/contribs/RELATIONAL-ARITHMETICS/add_gen.ma
index 225580da5..8037f8ba7 100644
--- a/matita/contribs/RELATIONAL-ARITHMETICS/add_gen.ma
+++ b/matita/contribs/RELATIONAL-ARITHMETICS/add_gen.ma
@@ -74,7 +74,7 @@ theorem add_gen_S_3: \forall p,q,r. add p q (S r) \to
    rewrite > H0. clear H0. clear r.
  ]; apply ex_intro; [| auto || auto ] (**)
 qed.
-
+(*
 (* alternative proofs invoking add_gen_2 *)
 
 variant add_gen_O_3_alt: \forall p,q. add p q O \to p = O \land q = O.
@@ -102,3 +102,27 @@ variant add_gen_S_3_alt: \forall p,q,r. add p q (S r) \to
    rewrite > H0. clear H0. clear r.
  ]; apply ex_intro; [| auto || auto ]. (**)
 qed.
+*)
+(* other simplification lemmas *)
+
+theorem add_gen_eq_2_3: \forall p,q. add p q q \to p = O.
+ intros 2. elim q; clear q; intros;
+ [ lapply add_gen_O_2 to H as H0. clear H.
+   rewrite > H0. clear H0. clear p
+ | lapply add_gen_S_2 to H1 as H0. clear H1.
+   decompose H0.
+   lapply eq_gen_S_S to H2 as H0. clear H2.
+   rewrite < H0 in H3. clear H0. clear a
+ ]; auto.
+qed.
+
+theorem add_gen_eq_1_3: \forall p,q. add p q p \to q = O.
+ intros 1. elim p; clear p; intros;
+ [ lapply add_gen_O_1 to H as H0. clear H.
+   rewrite > H0. clear H0. clear q
+ | lapply add_gen_S_1 to H1 as H0. clear H1.
+   decompose H0.
+   lapply eq_gen_S_S to H2 as H0. clear H2.
+   rewrite < H0 in H3. clear H0. clear a
+ ]; auto.
+qed.
diff --git a/matita/contribs/RELATIONAL-ARITHMETICS/add_props.ma b/matita/contribs/RELATIONAL-ARITHMETICS/add_props.ma
index e04d8f616..6d2bef823 100644
--- a/matita/contribs/RELATIONAL-ARITHMETICS/add_props.ma
+++ b/matita/contribs/RELATIONAL-ARITHMETICS/add_props.ma
@@ -48,7 +48,6 @@ theorem add_shift_S_sx: \forall p,q,r. add p (S q) r \to add (S p) q r.
  auto.
 qed.
 
-
 theorem add_shift_S_dx: \forall p,q,r. add (S p) q r \to add p (S q) r.
  intros.
  lapply add_gen_S_1 to H as H0. clear H.
@@ -104,22 +103,3 @@ theorem add_conf: \forall p,q,r1. add p q r1 \to
    rewrite > H2. clear H2. clear r2.
  ]; auto.
 qed.
-
-
-
-theorem add_gen_eq_2_3: \forall p,q. add p q q \to p = O.
- intros 2. elim q; clear q; intros;
- [ lapply add_gen_O_2 to H as H0. clear H.
-   rewrite > H0. clear H0. clear p
- | lapply add_gen_S_2 to H1 as H0. clear H1.
-   decompose H0.
-   lapply eq_gen_S_S to H2 as H0. clear H2.
-   rewrite < H0 in H3. clear H0. clear a
- ]; auto.
-qed.
-
-theorem add_gen_eq_1_3: \forall p,q. add p q p \to q = O.
- intros. 
- lapply add_sym to H. clear H.
- auto.
-qed.
diff --git a/matita/contribs/RELATIONAL-ARITHMETICS/nat_gen.ma b/matita/contribs/RELATIONAL-ARITHMETICS/nat_fwd.ma
similarity index 100%
rename from matita/contribs/RELATIONAL-ARITHMETICS/nat_gen.ma
rename to matita/contribs/RELATIONAL-ARITHMETICS/nat_fwd.ma
-- 
2.39.2