1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "basic_2/rt_transition/fpb_feqx.ma".
16 include "basic_2/rt_transition/fpbq.ma".
18 (* PARALLEL RST-TRANSITION FOR CLOSURES *************************************)
20 (* Properties with proper parallel rst-transition for closures **************)
23 ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ →
24 ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫.
25 #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
26 /3 width=1 by fpbq_fquq, fpbq_cpx, fpbq_lpx, fqu_fquq/
29 (* Basic_2A1: fpb_fpbq_alt *)
31 ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ →
32 ∧∧ ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫ & (❪G1,L1,T1❫ ≛ ❪G2,L2,T2❫ → ⊥).
33 /3 width=10 by fpb_fpbq, fpb_inv_feqx, conj/ qed-.
35 (* Inversrion lemmas with proper parallel rst-transition for closures *******)
37 (* Basic_2A1: uses: fpbq_ind_alt *)
39 ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫ →
40 ∨∨ ❪G1,L1,T1❫ ≛ ❪G2,L2,T2❫
41 | ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫.
42 #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
43 [ #G2 #L2 #T2 * [2: * #H1 #H2 #H3 destruct ]
44 /3 width=1 by fpb_fqu, feqx_intro_sn, or_intror, or_introl/
45 | #T2 #H elim (teqx_dec T1 T2)
46 /4 width=1 by fpb_cpx, feqx_intro_sn, or_intror, or_introl/
47 | #L2 elim (reqx_dec L1 L2 T1)
48 /4 width=1 by fpb_lpx, feqx_intro_sn, or_intror, or_introl/
49 | /2 width=1 by or_introl/
53 (* Basic_2A1: fpbq_inv_fpb_alt *)
54 lemma fpbq_fneqx_inv_fpb:
55 ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫ →
56 (❪G1,L1,T1❫ ≛ ❪G2,L2,T2❫ → ⊥) → ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫.
57 #G1 #G2 #L1 #L2 #T1 #T2 #H #H0
58 elim (fpbq_inv_fpb … H) -H // #H elim H0 -H0 //