1 (**************************************************************************)
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 *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "basic_2/reduction/cpx_lift.ma".
16 include "basic_2/reduction/cnx.ma".
18 (* NORMAL TERMS FOR CONTEXT-SENSITIVE EXTENDED REDUCTION ********************)
20 (* Relocation properties ****************************************************)
22 lemma cnx_lift: ∀h,g,G,L0,L,T,T0,s,d,e. ⦃G, L⦄ ⊢ ➡[h, g] 𝐍⦃T⦄ → ⇩[s, d, e] L0 ≡ L →
23 ⇧[d, e] T ≡ T0 → ⦃G, L0⦄ ⊢ ➡[h, g] 𝐍⦃T0⦄.
24 #h #g #G #L0 #L #T #T0 #s #d #e #HLT #HL0 #HT0 #X #H
25 elim (cpx_inv_lift1 … H … HL0 … HT0) -L0 #T1 #HT10 #HT1
26 <(HLT … HT1) in HT0; -L #HT0
27 >(lift_mono … HT10 … HT0) -T1 -X //
30 lemma cnx_inv_lift: ∀h,g,G,L0,L,T,T0,s,d,e. ⦃G, L0⦄ ⊢ ➡[h, g] 𝐍⦃T0⦄ → ⇩[s, d, e] L0 ≡ L →
31 ⇧[d, e] T ≡ T0 → ⦃G, L⦄ ⊢ ➡[h, g] 𝐍⦃T⦄.
32 #h #g #G #L0 #L #T #T0 #s #d #e #HLT0 #HL0 #HT0 #X #H
33 elim (lift_total X d e) #X0 #HX0
34 lapply (cpx_lift … H … HL0 … HT0 … HX0) -L #HTX0
35 >(HLT0 … HTX0) in HX0; -L0 -X0 #H
36 >(lift_inj … H … HT0) -T0 -X -d -e //