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/rpx_reqx.ma".
16 include "basic_2/rt_computation/cpxs.ma".
18 (* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
20 (* Properties with sort-irrelevant equivalence for terms ********************)
22 lemma teqx_cpxs_trans: ∀h,U1,T1. U1 ≛ T1 → ∀G,L,T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 →
23 ∃∃U2. ❪G,L❫ ⊢ U1 ⬈*[h] U2 & U2 ≛ T2.
24 #h #U1 #T1 #HUT1 #G #L #T2 #HT12 @(cpxs_ind … HT12) -T2 /2 width=3 by ex2_intro/
25 #T #T2 #_ #HT2 * #U #HU1 #HUT elim (teqx_cpx_trans … HUT … HT2) -T -T1
26 /3 width=3 by ex2_intro, cpxs_strap1/
29 (* Note: this requires teqx to be symmetric *)
30 (* Nasic_2A1: uses: cpxs_neq_inv_step_sn *)
31 lemma cpxs_tneqx_fwd_step_sn: ∀h,G,L,T1,T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) →
32 ∃∃T,T0. ❪G,L❫ ⊢ T1 ⬈[h] T & T1 ≛ T → ⊥ & ❪G,L❫ ⊢ T ⬈*[h] T0 & T0 ≛ T2.
33 #h #G #L #T1 #T2 #H @(cpxs_ind_dx … H) -T1
35 | #T1 #T0 #HT10 #HT02 #IH #Hn12
36 elim (teqx_dec T1 T0) [ -HT10 -HT02 #H10 | -IH #Hn10 ]
37 [ elim IH -IH /3 width=3 by teqx_trans/ -Hn12
38 #T3 #T4 #HT03 #Hn03 #HT34 #H42
39 elim (teqx_cpx_trans … H10 … HT03) -HT03 #T5 #HT15 #H53
40 elim (teqx_cpxs_trans … H53 … HT34) -HT34 #T6 #HT56 #H64
41 /5 width=8 by teqx_canc_sn, (* 2x *) teqx_trans, ex4_2_intro/
42 | /3 width=6 by ex4_2_intro/