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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/reducibility/cpr_lift.ma".
16 include "basic_2/computation/cprs.ma".
18 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
20 (* Advanced inversion lemmas ************************************************)
22 (* Basic_1: was: pr3_gen_lref *)
23 lemma cprs_inv_lref1: ∀L,T2,i. L ⊢ #i ➡* T2 →
25 ∃∃K,V1,T1. ⇩[0, i] L ≡ K. ⓓV1 &
29 #L #T2 #i #H @(cprs_ind … H) -T2 /2 width=1/
32 elim (cpr_inv_lref1 … HT2) -HT2 /2 width=1/
33 * #K #V1 #T1 #HLK #HVT1 #HT12 #Hi
34 @or_intror @(ex4_3_intro … HLK … HT12) // /3 width=3/ (**) (* explicit constructors *)
35 | * #K #V1 #T1 #HLK #HVT1 #HT1 #Hi
36 lapply (ldrop_fwd_ldrop2 … HLK) #H0LK
37 elim (cpr_inv_lift … H0LK … HT1 … HT2) -H0LK -T /4 width=6/
41 (* Basic_1: was: pr3_gen_abst *)
42 lemma cprs_inv_abst1: ∀I,W,L,V1,T1,U2. L ⊢ ⓛV1. T1 ➡* U2 →
43 ∃∃V2,T2. L ⊢ V1 ➡* V2 & L. ⓑ{I} W ⊢ T1 ➡* T2 &
45 #I #W #L #V1 #T1 #U2 #H @(cprs_ind … H) -U2 /2 width=5/
46 #U #U2 #_ #HU2 * #V #T #HV1 #HT1 #H destruct
47 elim (cpr_inv_abst1 … HU2 I W) -HU2 #V2 #T2 #HV2 #HT2 #H destruct /3 width=5/
50 (* Relocation properties ****************************************************)
52 (* Basic_1: was: pr3_lift *)
53 lemma cprs_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K → ∀T1,U1. ⇧[d, e] T1 ≡ U1 →
54 ∀T2. K ⊢ T1 ➡* T2 → ∀U2. ⇧[d, e] T2 ≡ U2 →
56 #L #K #d #e #HLK #T1 #U1 #HTU1 #T2 #HT12 @(cprs_ind … HT12) -T2
58 <(lift_mono … HTU1 … HT12) -T1 //
59 | -HTU1 #T #T2 #_ #HT2 #IHT2 #U2 #HTU2
60 elim (lift_total T d e) #U #HTU
61 lapply (cpr_lift … HLK … HTU … HTU2 … HT2) -T2 -HLK /3 width=3/
65 (* Basic_1: was: pr3_gen_lift *)
66 lemma cprs_inv_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K →
67 ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀U2. L ⊢ U1 ➡* U2 →
68 ∃∃T2. ⇧[d, e] T2 ≡ U2 & K ⊢ T1 ➡* T2.
69 #L #K #d #e #HLK #T1 #U1 #HTU1 #U2 #HU12 @(cprs_ind … HU12) -U2 /2 width=3/
70 -HTU1 #U #U2 #_ #HU2 * #T #HTU #HT1
71 elim (cpr_inv_lift … HLK … HTU … HU2) -U -HLK /3 width=5/