file names patched

diff --git a/matita/contribs/RELATIONAL-ARITHMETICS/add_fwd.ma b/matita/contribs/RELATIONAL-ARITHMETICS/add_fwd.ma
new file mode 100644 (file)
index 0000000..8037f8b
--- /dev/null
+++ b/matita/contribs/RELATIONAL-ARITHMETICS/add_fwd.ma
@@ -0,0 +1,128 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/RELATIONAL-ARITHMETICS/add_gen".
+
+include "nat_gen.ma".
+include "add_defs.ma".
+
+(* primitive generation lemmas proved by elimination and inversion *)
+
+theorem add_gen_O_1: \forall q,r. add O q r \to q = r.
+  intros. elim H; clear H; clear q; clear r; intros;
+ [ reflexivity
+ | clear H1. auto
+ ].
+qed.
+
+theorem add_gen_S_1: \forall p,q,r. add (S p) q r \to 
+                     \exists s. r = (S s) \land add p q s.
+ intros. elim H; clear H; clear q; clear r; intros;
+ [
+ | clear H1. 
+  decompose H2.
+  rewrite > H1. clear H1. clear n2
+ ]; apply ex_intro; [| auto || auto ]. (**)
+qed.
+
+theorem add_gen_O_2: \forall p,r. add p O r \to p = r.
+ intros. inversion H; clear H; intros;
+ [ auto
+ | clear H. clear H1.
+   lapply eq_gen_O_S to H2 as H0. apply H0
+ ].
+qed.
+
+theorem add_gen_S_2: \forall p,q,r. add p (S q) r \to 
+                     \exists s. r = (S s) \land add p q s.
+ intros. inversion H; clear H; intros;
+ [ lapply eq_gen_S_O to H as H0. apply H0
+ | clear H1. clear H3. clear r.
+   lapply eq_gen_S_S to H2 as H0. clear H2.
+   rewrite > H0. clear H0. clear q.
+   apply ex_intro; [| auto ] (**)
+ ].
+qed.
+
+theorem add_gen_O_3: \forall p,q. add p q O \to p = O \land q = O.
+ intros. inversion H; clear H; intros;
+ [ rewrite < H1. clear H1. clear p.
+   auto
+ | clear H. clear H1.
+   lapply eq_gen_O_S to H3 as H0. apply H0
+ ].
+qed.
+
+theorem add_gen_S_3: \forall p,q,r. add p q (S r) \to
+                     \exists s. p = S s \land add s q r \lor
+                                q = S s \land add p s r.
+ intros. inversion H; clear H; intros;
+ [ rewrite < H1. clear H1. clear p
+ | clear H1.
+   lapply eq_gen_S_S to H3 as H0. clear H3.
+   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.
+ intros 2. elim q; clear q; intros;
+ [ lapply add_gen_O_2 to H as H0. clear H.
+   rewrite > H0. clear H0. clear p.
+   auto
+ | clear H.
+   lapply add_gen_S_2 to H1 as H0. clear H1.
+   decompose H0.
+   lapply eq_gen_O_S to H1 as H0. apply H0
+ ].
+qed.
+
+variant add_gen_S_3_alt: \forall p,q,r. add p q (S r) \to
+                         \exists s. p = S s \land add s q r \lor
+                                    q = S s \land add p s r.
+ intros 2. elim q; clear q; intros;
+ [ lapply add_gen_O_2 to H as H0. clear H.
+   rewrite > H0. clear H0. clear p
+ | clear H.
+   lapply add_gen_S_2 to H1 as H0. clear H1.
+   decompose H0.
+   lapply eq_gen_S_S to H1 as H0. clear H1.
+   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_gen.ma b/matita/contribs/RELATIONAL-ARITHMETICS/add_gen.ma
deleted file mode 100644 (file)
index 8037f8b..0000000
--- a/matita/contribs/RELATIONAL-ARITHMETICS/add_gen.ma
+++ /dev/null
@@ -1,128 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-set "baseuri" "cic:/matita/RELATIONAL-ARITHMETICS/add_gen".
-
-include "nat_gen.ma".
-include "add_defs.ma".
-
-(* primitive generation lemmas proved by elimination and inversion *)
-
-theorem add_gen_O_1: \forall q,r. add O q r \to q = r.
-  intros. elim H; clear H; clear q; clear r; intros;
- [ reflexivity
- | clear H1. auto
- ].
-qed.
-
-theorem add_gen_S_1: \forall p,q,r. add (S p) q r \to 
-                     \exists s. r = (S s) \land add p q s.
- intros. elim H; clear H; clear q; clear r; intros;
- [
- | clear H1. 
-  decompose H2.
-  rewrite > H1. clear H1. clear n2
- ]; apply ex_intro; [| auto || auto ]. (**)
-qed.
-
-theorem add_gen_O_2: \forall p,r. add p O r \to p = r.
- intros. inversion H; clear H; intros;
- [ auto
- | clear H. clear H1.
-   lapply eq_gen_O_S to H2 as H0. apply H0
- ].
-qed.
-
-theorem add_gen_S_2: \forall p,q,r. add p (S q) r \to 
-                     \exists s. r = (S s) \land add p q s.
- intros. inversion H; clear H; intros;
- [ lapply eq_gen_S_O to H as H0. apply H0
- | clear H1. clear H3. clear r.
-   lapply eq_gen_S_S to H2 as H0. clear H2.
-   rewrite > H0. clear H0. clear q.
-   apply ex_intro; [| auto ] (**)
- ].
-qed.
-
-theorem add_gen_O_3: \forall p,q. add p q O \to p = O \land q = O.
- intros. inversion H; clear H; intros;
- [ rewrite < H1. clear H1. clear p.
-   auto
- | clear H. clear H1.
-   lapply eq_gen_O_S to H3 as H0. apply H0
- ].
-qed.
-
-theorem add_gen_S_3: \forall p,q,r. add p q (S r) \to
-                     \exists s. p = S s \land add s q r \lor
-                                q = S s \land add p s r.
- intros. inversion H; clear H; intros;
- [ rewrite < H1. clear H1. clear p
- | clear H1.
-   lapply eq_gen_S_S to H3 as H0. clear H3.
-   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.
- intros 2. elim q; clear q; intros;
- [ lapply add_gen_O_2 to H as H0. clear H.
-   rewrite > H0. clear H0. clear p.
-   auto
- | clear H.
-   lapply add_gen_S_2 to H1 as H0. clear H1.
-   decompose H0.
-   lapply eq_gen_O_S to H1 as H0. apply H0
- ].
-qed.
-
-variant add_gen_S_3_alt: \forall p,q,r. add p q (S r) \to
-                         \exists s. p = S s \land add s q r \lor
-                                    q = S s \land add p s r.
- intros 2. elim q; clear q; intros;
- [ lapply add_gen_O_2 to H as H0. clear H.
-   rewrite > H0. clear H0. clear p
- | clear H.
-   lapply add_gen_S_2 to H1 as H0. clear H1.
-   decompose H0.
-   lapply eq_gen_S_S to H1 as H0. clear H1.
-   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.