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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/reduction/cpr_lift.ma".
16 include "basic_2/reduction/cnf.ma".
18 (* CONTEXT-SENSITIVE NORMAL TERMS *******************************************)
20 (* Advanced properties ******************************************************)
22 (* Basic_1: was only: nf2_csort_lref *)
23 lemma cnf_lref_atom: ∀L,i. ⇩[0, i] L ≡ ⋆ → L ⊢ 𝐍⦃#i⦄.
25 elim (cpr_inv_lref1 … H) -H // *
27 lapply (ldrop_mono … HL … HLK) -L #H destruct
30 (* Basic_1: was: nf2_lref_abst *)
31 lemma cnf_lref_abst: ∀L,K,V,i. ⇩[0, i] L ≡ K. ⓛV → L ⊢ 𝐍⦃#i⦄.
32 #L #K #V #i #HLK #X #H
33 elim (cpr_inv_lref1 … H) -H // *
34 #K0 #V1 #V2 #HLK0 #_ #_
35 lapply (ldrop_mono … HLK … HLK0) -L #H destruct
38 (* Relocation properties ****************************************************)
40 (* Basic_1: was: nf2_lift *)
41 lemma cnf_lift: ∀L0,L,T,T0,d,e.
42 L ⊢ 𝐍⦃T⦄ → ⇩[d, e] L0 ≡ L → ⇧[d, e] T ≡ T0 → L0 ⊢ 𝐍⦃T0⦄.
43 #L0 #L #T #T0 #d #e #HLT #HL0 #HT0 #X #H
44 elim (cpr_inv_lift1 … H … HL0 … HT0) -L0 #T1 #HT10 #HT1
45 <(HLT … HT1) in HT0; -L #HT0
46 >(lift_mono … HT10 … HT0) -T1 -X //