]> matita.cs.unibo.it Git - helm.git/blob - matita/matita/contribs/lambdadelta/basic_2/etc/fpn/bteq_bteq.etc
- ynat: some additions
[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / fpn / bteq_bteq.etc
1 (**************************************************************************)
2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
5 (*      ||T||                                                             *)
6 (*      ||I||       Developers:                                           *)
7 (*      ||T||         The HELM team.                                      *)
8 (*      ||A||         http://helm.cs.unibo.it                             *)
9 (*      \   /                                                             *)
10 (*       \ /        This file is distributed under the terms of the       *)
11 (*        v         GNU General Public License Version 2                  *)
12 (*                                                                        *)
13 (**************************************************************************)
14
15 include "basic_2/grammar/bteq.ma".
16
17 (* EQUIVALENT "BIG TREE" NORMAL FORMS ***************************************)
18
19 (* Main properties **********************************************************)
20
21 theorem bteq_trans: tri_transitive … bteq.
22 #G1 #G #L1 #L #T1 #T * //
23 qed-.
24
25 theorem bteq_canc_sn: ∀G,G1,G2,L,L1,L2,T,T1,T2. ⦃G, L, T⦄ ⋕ ⦃G1, L1, T1⦄ →
26                       ⦃G, L, T⦄ ⋕ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄.
27 /3 width=5 by bteq_trans, bteq_sym/ qed-.
28
29 theorem bteq_canc_dx: ∀G1,G2,G,L1,L2,L,T1,T2,T. ⦃G1, L1, T1⦄ ⋕ ⦃G, L, T⦄ →
30                       ⦃G2, L2, T2⦄ ⋕ ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄.
31 /3 width=5 by bteq_trans, bteq_sym/ qed-.