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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 *)
10 (* \ / This file is distributed under the terms of the *)
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15 include "basic_2/rt_computation/cpxs_teqx.ma".
16 include "basic_2/rt_computation/cpxs_cpxs.ma".
17 include "basic_2/rt_computation/csx_csx.ma".
19 (* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
21 (* Properties with unbound context-sensitive rt-computation for terms *******)
23 (* Basic_1: was just: sn3_intro *)
24 lemma csx_intro_cpxs (h) (G) (L):
25 ∀T1. (∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → ❪G,L❫ ⊢ ⬈*𝐒[h] T2) →
27 /4 width=1 by cpx_cpxs, csx_intro/ qed-.
29 (* Basic_1: was just: sn3_pr3_trans *)
30 lemma csx_cpxs_trans (h) (G) (L):
31 ∀T1. ❪G,L❫ ⊢ ⬈*𝐒[h] T1 →
32 ∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → ❪G,L❫ ⊢ ⬈*𝐒[h] T2.
33 #h #G #L #T1 #HT1 #T2 #H @(cpxs_ind … H) -T2
34 /2 width=3 by csx_cpx_trans/
37 (* Eliminators with unbound context-sensitive rt-computation for terms ******)
39 lemma csx_ind_cpxs_teqx (h) (G) (L):
41 (∀T1. ❪G,L❫ ⊢ ⬈*𝐒[h] T1 →
42 (∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
44 ∀T1. ❪G,L❫ ⊢ ⬈*𝐒[h] T1 →
45 ∀T0. ❪G,L❫ ⊢ T1 ⬈*[h] T0 → ∀T2. T0 ≛ T2 → Q T2.
46 #h #G #L #Q #IH #T1 #H @(csx_ind … H) -T1
47 #T1 #HT1 #IH1 #T0 #HT10 #T2 #HT02
48 @IH -IH /3 width=3 by csx_cpxs_trans, csx_teqx_trans/ -HT1 #V2 #HTV2 #HnTV2
49 lapply (teqx_tneqx_trans … HT02 … HnTV2) -HnTV2 #H
50 elim (teqx_cpxs_trans … HT02 … HTV2) -T2 #V0 #HTV0 #HV02
51 lapply (tneqx_teqx_canc_dx … H … HV02) -H #HnTV0
52 elim (teqx_dec T1 T0) #H
53 [ lapply (teqx_tneqx_trans … H … HnTV0) -H -HnTV0 #Hn10
54 lapply (cpxs_trans … HT10 … HTV0) -T0 #H10
55 elim (cpxs_tneqx_fwd_step_sn … H10 … Hn10) -H10 -Hn10
56 /3 width=8 by teqx_trans/
57 | elim (cpxs_tneqx_fwd_step_sn … HT10 … H) -HT10 -H #T #V #HT1 #HnT1 #HTV #HVT0
58 elim (teqx_cpxs_trans … HVT0 … HTV0) -T0
59 /3 width=8 by cpxs_trans, teqx_trans/
63 (* Basic_2A1: was: csx_ind_alt *)
64 lemma csx_ind_cpxs (h) (G) (L) (Q:predicate …):
65 (∀T1. ❪G,L❫ ⊢ ⬈*𝐒[h] T1 →
66 (∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
68 ∀T. ❪G,L❫ ⊢ ⬈*𝐒[h] T → Q T.
69 #h #G #L #Q #IH #T #HT
70 @(csx_ind_cpxs_teqx … IH … HT) -IH -HT // (**) (* full auto fails *)