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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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17 include "NPlus/inv.ma".
19 (* Functional properties ****************************************************)
21 theorem nplus_total: ∀p,q. ∃r. p ⊕ q ≍ r.
22 intros; elim q; clear q;
23 [ autobatch | decompose; autobatch ].
26 theorem nplus_mono: ∀p,q,r1. p ⊕ q ≍ r1 →
27 ∀r2. p ⊕ q ≍ r2 → r1 = r2.
28 intros 4; elim H; clear H q r1;
29 [ lapply linear nplus_inv_zero_2 to H1
30 | lapply linear nplus_inv_succ_2 to H3. decompose
31 ]; destruct; autobatch.
34 theorem nplus_inj_1: ∀p1, q, r. p1 ⊕ q ≍ r →
35 ∀p2. p2 ⊕ q ≍ r → p2 = p1.
36 intros 4; elim H; clear H q r;
37 [ lapply linear nplus_inv_zero_2 to H1
38 | lapply linear nplus_inv_succ_2_3 to H3