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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_2A/reduction/cpr_lift.ma".
16 include "basic_2A/computation/cprs.ma".
18 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
20 (* Advanced properties ******************************************************)
22 lemma cprs_delta: ∀G,L,K,V,V2,i.
23 ⬇[i] L ≡ K.ⓓV → ⦃G, K⦄ ⊢ V ➡* V2 →
24 ∀W2. ⬆[0, i + 1] V2 ≡ W2 → ⦃G, L⦄ ⊢ #i ➡* W2.
25 #G #L #K #V #V2 #i #HLK #H elim H -V2 [ /3 width=6 by cpr_cprs, cpr_delta/ ]
26 #V1 #V2 #_ #HV12 #IHV1 #W2 #HVW2
27 lapply (drop_fwd_drop2 … HLK) -HLK #HLK
28 elim (lift_total V1 0 (i+1)) /4 width=12 by cpr_lift, cprs_strap1/
31 (* Advanced inversion lemmas ************************************************)
33 (* Basic_1: was: pr3_gen_lref *)
34 lemma cprs_inv_lref1: ∀G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡* T2 →
36 ∃∃K,V1,T1. ⬇[i] L ≡ K.ⓓV1 & ⦃G, K⦄ ⊢ V1 ➡* T1 &
38 #G #L #T2 #i #H @(cprs_ind … H) -T2 /2 width=1 by or_introl/
41 elim (cpr_inv_lref1 … HT2) -HT2 /2 width=1 by or_introl/
42 * /4 width=6 by cpr_cprs, ex3_3_intro, or_intror/
43 | * #K #V1 #T1 #HLK #HVT1 #HT1
44 lapply (drop_fwd_drop2 … HLK) #H0LK
45 elim (cpr_inv_lift1 … HT2 … H0LK … HT1) -H0LK -T
46 /4 width=6 by cprs_strap1, ex3_3_intro, or_intror/
50 (* Relocation properties ****************************************************)
52 (* Basic_1: was: pr3_lift *)
53 lemma cprs_lift: ∀G. d_liftable (cprs G).
54 /3 width=10 by d_liftable_LTC, cpr_lift/ qed.
56 (* Basic_1: was: pr3_gen_lift *)
57 lemma cprs_inv_lift1: ∀G. d_deliftable_sn (cprs G).
58 /3 width=6 by d_deliftable_sn_LTC, cpr_inv_lift1/