X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FRELATIONAL%2FNPlus%2Fmonoid.ma;fp=helm%2Fsoftware%2Fmatita%2Fcontribs%2FRELATIONAL%2FNPlus%2Fmonoid.ma;h=0000000000000000000000000000000000000000;hb=da0775e27b362e91ea1453a800bc403781cc2ca3;hp=7a9bb8da047c4ee1443eef83ae70691cc6f5c504;hpb=d9824956d9132109ed5f23380a0a1f9c5181d18a;p=helm.git

diff --git a/helm/software/matita/contribs/RELATIONAL/NPlus/monoid.ma b/helm/software/matita/contribs/RELATIONAL/NPlus/monoid.ma
deleted file mode 100644
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-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-
-
-include "NPlus/fun.ma".
-
-(* Monoidal properties ******************************************************)
-
-theorem nplus_zero_1: ∀q. zero ⊕ q ≍ q.
- intros; elim q; clear q; autobatch.
-qed.
-
-theorem nplus_succ_1: ∀p,q,r. p ⊕ q ≍ r → succ p ⊕ q ≍ succ r.
- intros; elim H; clear H q r; autobatch.
-qed.
-
-theorem nplus_comm: ∀p, q, x. p ⊕ q ≍ x → ∀y. q ⊕ p ≍ y → x = y.
- intros 4; elim H; clear H q x;
- [ lapply linear nplus_inv_zero_1 to H1
- | lapply linear nplus_inv_succ_1 to H3. decompose
- ]; destruct; autobatch.
-qed.
-
-theorem nplus_comm_rew: ∀p,q,r. p ⊕ q ≍ r → q ⊕ p ≍ r.
- intros; elim H; clear H q r; autobatch.
-qed.
-
-theorem nplus_ass: ∀p1, p2, r1. p1 ⊕ p2 ≍ r1 → ∀p3, s1. r1 ⊕ p3 ≍ s1 →
-                   ∀r3. p2 ⊕ p3 ≍ r3 → ∀s3. p1 ⊕ r3 ≍ s3 → s1 = s3.
- intros 4; elim H; clear H p2 r1;
- [ lapply linear nplus_inv_zero_1 to H2. destruct.
-   lapply nplus_mono to H1, H3. destruct. autobatch
- | lapply linear nplus_inv_succ_1 to H3. decompose. destruct.
-   lapply linear nplus_inv_succ_1 to H4. decompose. destruct.
-   lapply linear nplus_inv_succ_2 to H5. decompose. destruct. autobatch
- ].
-qed.
- 
-(* Corollaries of functional properties **************************************)
-
-theorem nplus_inj_2: ∀p, q1, r. p ⊕ q1 ≍ r → ∀q2. p ⊕ q2 ≍ r → q1 = q2.
- intros. autobatch.
-qed.
-
-(* Corollaries of nonoidal properties ***************************************)
-
-theorem nplus_comm_1: ∀p1, q, r1. p1 ⊕ q ≍ r1 → ∀p2, r2. p2 ⊕ q ≍ r2 →
-                      ∀x. p2 ⊕ r1 ≍ x → ∀y. p1 ⊕ r2 ≍ y → x = y.
- intros 4; elim H; clear H q r1;
- [ lapply linear nplus_inv_zero_2 to H1
- | lapply linear nplus_inv_succ_2 to H3.
-   lapply linear nplus_inv_succ_2 to H4. decompose. destruct.
-   lapply linear nplus_inv_succ_2 to H5. decompose
- ]; destruct; autobatch.
-qed.
-
-theorem nplus_comm_1_rew: ∀p1,q,r1. p1 ⊕ q ≍ r1 → ∀p2,r2. p2 ⊕ q ≍ r2 →
-                          ∀s. p1 ⊕ r2 ≍ s → p2 ⊕ r1 ≍ s.
- intros 4; elim H; clear H q r1;
- [ lapply linear nplus_inv_zero_2 to H1. destruct
- | lapply linear nplus_inv_succ_2 to H3. decompose. destruct.
-   lapply linear nplus_inv_succ_2 to H4. decompose. destruct
- ]; autobatch.
-qed.
-
-(*                      
-theorem nplus_shift_succ_sx: \forall p,q,r. 
-                             (p \oplus (succ q) \asymp r) \to (succ p) \oplus q \asymp r.
- intros.
- lapply linear nplus_inv_succ_2 to H as H0.
- decompose. destruct. auto new timeout=100.
-qed.
-
-theorem nplus_shift_succ_dx: \forall p,q,r. 
-                             ((succ p) \oplus q \asymp r) \to p \oplus (succ q) \asymp r.
- intros.
- lapply linear nplus_inv_succ_1 to H as H0.
- decompose. destruct. auto new timeout=100.
-qed.
-
-theorem nplus_trans_1: \forall p,q1,r1. (p \oplus q1 \asymp r1) \to 
-                       \forall q2,r2. (r1 \oplus q2 \asymp r2) \to
-                       \exists q. (q1 \oplus q2 \asymp q) \land p \oplus q \asymp r2.
- intros 2; elim q1; clear q1; intros;
- [ lapply linear nplus_inv_zero_2 to H as H0.
-   destruct.
- | lapply linear nplus_inv_succ_2 to H1 as H0.
-   decompose. destruct.
-   lapply linear nplus_inv_succ_1 to H2 as H0.
-   decompose. destruct.
-   lapply linear H to H4, H3 as H0.
-   decompose.
- ]; apply ex_intro; [| auto new timeout=100 || auto new timeout=100 ]. (**)
-qed.
-
-theorem nplus_trans_2: ∀p1,q,r1. p1 ⊕ q ≍ r1 → ∀p2,r2. p2 ⊕ r1 ≍ r2 →
-                       ∃p. p1 ⊕ p2 ≍ p ∧ p ⊕ q ≍ r2.
- intros 2; elim q; clear q; intros;
- [ lapply linear nplus_inv_zero_2 to H as H0.
-   destruct
- | lapply linear nplus_inv_succ_2 to H1 as H0.
-   decompose. destruct.
-   lapply linear nplus_inv_succ_2 to H2 as H0.
-   decompose. destruct.
-   lapply linear H to H4, H3 as H0.
-   decompose.
- ]; autobatch. apply ex_intro; [| auto new timeout=100 || auto new timeout=100 ]. (**)
-qed.
-*)