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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "basic_2A/reduction/cpr_lift.ma".
16 include "basic_2A/reduction/cnr.ma".
18 (* NORMAL TERMS FOR CONTEXT-SENSITIVE REDUCTION *****************************)
20 (* Advanced properties ******************************************************)
22 lemma cnr_lref_abst: ∀G,L,K,V,i. ⬇[i] L ≡ K. ⓛV → ⦃G, L⦄ ⊢ ➡ 𝐍⦃#i⦄.
23 #G #L #K #V #i #HLK #X #H
24 elim (cpr_inv_lref1 … H) -H // *
25 #K0 #V1 #V2 #HLK0 #_ #_
26 lapply (drop_mono … HLK … HLK0) -L #H destruct
29 (* Relocation properties ****************************************************)
31 lemma cnr_lift: ∀G,L0,L,T,T0,s,l,m. ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄ →
32 ⬇[s, l, m] L0 ≡ L → ⬆[l, m] T ≡ T0 → ⦃G, L0⦄ ⊢ ➡ 𝐍⦃T0⦄.
33 #G #L0 #L #T #T0 #s #l #m #HLT #HL0 #HT0 #X #H
34 elim (cpr_inv_lift1 … H … HL0 … HT0) -L0 #T1 #HT10 #HT1
35 >(HLT … HT1) in HT0; -L #HT0
36 >(lift_mono … HT10 … HT0) -T1 -X //
39 lemma cnr_inv_lift: ∀G,L0,L,T,T0,s,l,m. ⦃G, L0⦄ ⊢ ➡ 𝐍⦃T0⦄ →
40 ⬇[s, l, m] L0 ≡ L → ⬆[l, m] T ≡ T0 → ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄.
41 #G #L0 #L #T #T0 #s #l #m #HLT0 #HL0 #HT0 #X #H
42 elim (lift_total X l m) #X0 #HX0
43 lapply (cpr_lift … H … HL0 … HT0 … HX0) -L #HTX0
44 <(HLT0 … HTX0) in HX0; -L0 -X0 #H
45 >(lift_inj … H … HT0) -T0 -X -s -l -m //