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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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15 include "basic_2/rt_transition/rpx_reqx.ma".
16 include "basic_2/rt_computation/cpxs.ma".
18 (* EXTENDED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS *************)
20 (* Properties with sort-irrelevant equivalence for terms ********************)
22 lemma teqx_cpxs_trans (G) (L) (T):
23 ∀T1. T1 ≛ T → ∀T2. ❪G,L❫ ⊢ T ⬈* T2 → ❪G,L❫ ⊢ T1 ⬈* T2.
24 #G #L #T #T1 #HT1 #T2 #HT2 @(cpxs_ind … HT2) -T2
25 [ /3 width=1 by teqx_cpx, cpx_cpxs/
26 | /2 width=3 by cpxs_strap1/
30 (* Note: this requires teqx to be symmetric *)
31 (* Nasic_2A1: uses: cpxs_neq_inv_step_sn *)
32 lemma cpxs_tneqx_fwd_step_sn (G) (L):
33 ∀T1,T2. ❪G,L❫ ⊢ T1 ⬈* T2 → (T1 ≛ T2 → ⊥) →
34 ∃∃T. ❪G,L❫ ⊢ T1 ⬈ T & T1 ≛ T → ⊥ & ❪G,L❫ ⊢ T ⬈* T2.
35 #G #L #T1 #T2 #H @(cpxs_ind_dx … H) -T1
37 | #T1 #T0 #HT10 #HT02 #IH #HnT12
38 elim (teqx_dec T1 T0) [ -HT10 -HT02 #HT10 | -IH #HnT10 ]
39 [ elim IH -IH /3 width=3 by teqx_trans/ -HnT12
41 lapply (teqx_cpx_trans … HT10 … HT0) -HT0 #HT1
42 /4 width=4 by teqx_canc_sn, ex3_intro/
43 | /3 width=4 by ex3_intro/