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/reduction/cpr_lift.ma".
16 include "basic_2/computation/cprs.ma".
18 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
20 (* Advanced properties ******************************************************)
22 (* Note: apparently this was missing in basic_1 *)
23 lemma cprs_delta: ∀G,L,K,V,V2,i.
24 ⇩[i] L ≡ K.ⓓV → ⦃G, K⦄ ⊢ V ➡* V2 →
25 ∀W2. ⇧[0, i + 1] V2 ≡ W2 → ⦃G, L⦄ ⊢ #i ➡* W2.
26 #G #L #K #V #V2 #i #HLK #H elim H -V2 [ /3 width=6 by cpr_cprs, cpr_delta/ ]
27 #V1 #V2 #_ #HV12 #IHV1 #W2 #HVW2
28 lapply (ldrop_fwd_drop2 … HLK) -HLK #HLK
29 elim (lift_total V1 0 (i+1)) /4 width=12 by cpr_lift, cprs_strap1/
32 (* Advanced inversion lemmas ************************************************)
34 (* Basic_1: was: pr3_gen_lref *)
35 lemma cprs_inv_lref1: ∀G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡* T2 →
37 ∃∃K,V1,T1. ⇩[i] L ≡ K.ⓓV1 & ⦃G, K⦄ ⊢ V1 ➡* T1 &
39 #G #L #T2 #i #H @(cprs_ind … H) -T2 /2 width=1 by or_introl/
42 elim (cpr_inv_lref1 … HT2) -HT2 /2 width=1 by or_introl/
43 * /4 width=6 by cpr_cprs, ex3_3_intro, or_intror/
44 | * #K #V1 #T1 #HLK #HVT1 #HT1
45 lapply (ldrop_fwd_drop2 … HLK) #H0LK
46 elim (cpr_inv_lift1 … HT2 … H0LK … HT1) -H0LK -T
47 /4 width=6 by cprs_strap1, ex3_3_intro, or_intror/
51 (* Relocation properties ****************************************************)
53 (* Basic_1: was: pr3_lift *)
54 lemma cprs_lift: ∀G. l_liftable (cprs G).
55 /3 width=10 by l_liftable_LTC, cpr_lift/ qed.
57 (* Basic_1: was: pr3_gen_lift *)
58 lemma cprs_inv_lift1: ∀G. l_deliftable_sn (cprs G).
59 /3 width=6 by l_deliftable_sn_LTC, cpr_inv_lift1/