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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 *)
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15 include "basic_2/reduction/cpx_lift.ma".
16 include "basic_2/computation/cpxs.ma".
18 (* CONTEXT-SENSITIVE EXTENDED PARALLEL COMPUTATION ON TERMS *****************)
20 (* Advanced properties ******************************************************)
22 lemma cpxs_delta: ∀h,g,I,L,K,V,V2,i.
23 ⇩[0, i] L ≡ K. ⓑ{I}V → ⦃h, K⦄ ⊢ V ➡*[g] V2 →
24 ∀W2. ⇧[0, i + 1] V2 ≡ W2 → ⦃h, L⦄ ⊢ #i ➡*[g] W2.
25 #h #g #I #L #K #V #V2 #i #HLK #H elim H -V2 [ /3 width=9/ ]
26 #V1 #V2 #_ #HV12 #IHV1 #W2 #HVW2
27 lapply (ldrop_fwd_ldrop2 … HLK) -HLK #HLK
28 elim (lift_total V1 0 (i+1)) /4 width=11 by cpx_lift, cpxs_strap1/
31 (* Advanced inversion lemmas ************************************************)
33 lemma cpxs_inv_lref1: ∀h,g,L,T2,i. ⦃h, L⦄ ⊢ #i ➡*[g] T2 →
35 ∃∃I,K,V1,T1. ⇩[0, i] L ≡ K.ⓑ{I}V1 & ⦃h, K⦄ ⊢ V1 ➡*[g] T1 &
37 #h #g #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1/
40 elim (cpx_inv_lref1 … HT2) -HT2 /2 width=1/
42 | * #I #K #V1 #T1 #HLK #HVT1 #HT1
43 lapply (ldrop_fwd_ldrop2 … HLK) #H0LK
44 elim (cpx_inv_lift1 … HT2 … H0LK … HT1) -H0LK -T /4 width=7/
48 (* Relocation properties ****************************************************)
50 (* Basic_1: was: pr3_lift *)
51 lemma cpxs_lift: ∀h,g. l_liftable (cpxs h g).
54 (* Basic_1: was: pr3_gen_lift *)
55 lemma cpxs_inv_lift1: ∀h,g. l_deliftable_sn (cpxs h g).
56 /3 width=5 by l_deliftable_sn_LTC, cpx_inv_lift1/
59 (* Properties on supclosure *************************************************)
61 include "basic_2/substitution/fsups.ma".
63 lemma fsupq_cpxs_trans: ∀h,g,L1,L2,T2,U2. ⦃h, L2⦄ ⊢ T2 ➡*[g] U2 →
64 ∀T1. ⦃L1, T1⦄ ⊃⸮ ⦃L2, T2⦄ →
65 ∃∃U1. ⦃h, L1⦄ ⊢ T1 ➡*[g] U1 & ⦃L1, U1⦄ ⊃* ⦃L2, U2⦄.
66 #h #g #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 [ /3 width=3/ ]
67 #T #T2 #HT2 #_ #IHTU2 #T1 #HT1
68 elim (fsupq_cpx_trans … HT1 … HT2) -T #T #HT1 #HT2
69 elim (IHTU2 … HT2) -T2 /3 width=3/
72 lemma fsup_ssta_trans: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ →
73 ∀U2,l. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l+1, U2⦄ →
74 ∃∃U1. ⦃h, L1⦄ ⊢ T1 ➡[g] U1 & ⦃L1, U1⦄ ⊃⸮ ⦃L2, U2⦄.
75 /3 width=4 by fsup_cpx_trans, ssta_cpx/ qed-.