+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||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/inv.ma".
-
-(* Functional properties ****************************************************)
-
-theorem nplus_total: ∀p,q. ∃r. p ⊕ q ≍ r.
- intros; elim q; clear q;
- [ autobatch | decompose; autobatch ].
-qed.
-
-theorem nplus_mono: ∀p,q,r1. p ⊕ q ≍ r1 →
- ∀r2. p ⊕ q ≍ r2 → r1 = r2.
- intros 4; elim H; clear H q r1;
- [ lapply linear nplus_inv_zero_2 to H1
- | lapply linear nplus_inv_succ_2 to H3. decompose
- ]; destruct; autobatch.
-qed.
-
-theorem nplus_inj_1: ∀p1, q, r. p1 ⊕ q ≍ r →
- ∀p2. p2 ⊕ q ≍ r → p2 = p1.
- intros 4; elim H; clear H q r;
- [ lapply linear nplus_inv_zero_2 to H1
- | lapply linear nplus_inv_succ_2_3 to H3
- ]; autobatch.
-qed.