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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/unfold/delift_delift.ma".
16 include "basic_2/computation/cprs_delift.ma".
17 include "basic_2/equivalence/cpcs_cpcs.ma".
19 (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
21 (* Properties on inverse basic term relocation ******************************)
23 lemma cpcs_zeta_delift_comm: ∀L,V,T1,T2. L.ⓓV ⊢ T1 ▼*[O, 1] ≡ T2 →
27 (* Basic_1: was only: pc3_gen_cabbr *)
28 lemma thin_cpcs_delift_mono: ∀L,U1,U2. L ⊢ U1 ⬌* U2 →
29 ∀K,d,e. L ▼*[d, e] ≡ K → ∀T1. L ⊢ U1 ▼*[d, e] ≡ T1 →
30 ∀T2. L ⊢ U2 ▼*[d, e] ≡ T2 → K ⊢ T1 ⬌* T2.
31 #L #U1 #U2 #H #K #d #e #HLK #T1 #HTU1 #T2 #HTU2
32 elim (cpcs_inv_cprs … H) -H #U #HU1 #HU2
33 elim (thin_cprs_delift_conf … HU1 … HLK … HTU1) -U1 #T #HT1 #HUT
34 elim (thin_cprs_delift_conf … HU2 … HLK … HTU2) -U2 -HLK #X #HT2 #H
35 lapply (delift_mono … H … HUT) -L #H destruct /2 width=3/