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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 *)
11 (* v GNU General Public License Version 2 *)
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15 include "basic_2/grammar/tstc_vector.ma".
16 include "basic_2/substitution/lift_vector.ma".
17 include "basic_2/computation/cprs_tstc.ma".
19 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
21 (* Vector form of forward lemmas involving same top term constructor ********)
23 lemma cpr_fwd_beta_vector: ∀L,V,W,T,U,Vs. L ⊢ ⒶVs. ⓐV. ⓛW. T ➡ U →
24 ⒶVs. ⓐV. ⓛW. T ≃ U ∨ L ⊢ ⒶVs. ⓓV. T ➡* U.
25 #L #V #W #T #U * /2 width=1 by cpr_fwd_beta/
27 elim (cpr_inv_appl1_simple … H ?) -H
28 [ #V1 #T1 #_ #_ #H destruct /2 width=1/
33 lemma cpr_fwd_theta_vector: ∀L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
34 ∀V,T,U. L ⊢ ⒶV1s. ⓓV. T ➡ U →
35 ⒶV1s. ⓓV. T ≃ U ∨ L ⊢ ⓓV. ⒶV2s. T ➡* U.
36 #L #V1s #V2s * -V1s -V2s /3 width=1/
37 #V1s #V2s #V1a #V2a #HV12a * -V1s -V2s /2 width=1 by cpr_fwd_theta/ -HV12a
38 #V1s #V2s #V1b #V2b #_ #_ #V #U #T #H
39 elim (cpr_inv_appl1_simple … H ?) -H //
40 #V0 #T0 #_ #_ #H destruct /2 width=1/
44 (* Basic_1: was: pr3_iso_appls_cast *)
45 lemma cprs_fwd_tau_vector: ∀L,Vs,W,T,U. L ⊢ ⒶVs. ⓣW. T ➡* U →
46 ⒶVs. ⓣW. T ≃ U ∨ L ⊢ ⒶVs. T ➡* U.
47 #L #Vs elim Vs -Vs /2 width=1 by cprs_fwd_tau/
48 #V #Vs #IHVs #W #T #U #H
49 elim (cprs_inv_appl1 … H) -H *
50 [ -IHVs #V0 #T0 #_ #_ #H destruct /2 width=1/
51 | #V0 #W0 #T0 #HV0 #HT0 #HU
52 elim (IHVs … HT0) -IHVs -HT0 #HT0
53 [ elim (tstc_inv_bind_appls_simple … HT0 ?) //
55 @(cprs_trans … HU) -HU
56 @(cprs_strap1 … (ⓐV0.ⓛW0.T0)) /2 width=1/ -HV0 -HT0 /3 width=1/
58 | #V0 #V1 #V2 #T0 #HV0 #HV01 #HT0 #HU
59 elim (IHVs … HT0) -IHVs -HT0 #HT0
60 [ elim (tstc_inv_bind_appls_simple … HT0 ?) //
62 @(cprs_trans … HU) -HU
63 @(cprs_strap1 … (ⓐV0.ⓓV2.T0)) /2 width=1/ -HV0 -HT0 /3 width=3/
67 axiom cprs_fwd_theta_vector: ∀L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
68 ∀V,T,U. L ⊢ ⒶV1s. ⓓV. T ➡* U →
69 ⒶV1s. ⓓV. T ≃ U ∨ L ⊢ ⓓV. ⒶV2s. T ➡* U.