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 "static_2/relocation/lifts_teqw.ma".
16 include "basic_2/rt_computation/cpms_drops.ma".
17 include "basic_2/rt_computation/cnuw.ma".
19 (* NORMAL TERMS FOR T-UNUNBOUND WHD RT-TRANSITION ***************************)
21 (* Properties with generic relocation ***************************************)
23 lemma cnuw_lifts (h) (G): d_liftable1 … (cnuw h G).
24 #h #G #K #T #HT #b #f #L #HLK #U #HTU #n #U0 #H
25 elim (cpms_inv_lifts_sn … H … HLK … HTU) -b -L #T0 #HTU0 #HT0
26 lapply (HT … HT0) -G -K /2 width=6 by teqw_lifts_bi/
29 (* Inversion lemmas with generic relocation *********************************)
31 lemma cnuw_inv_lifts (h) (G): d_deliftable1 … (cnuw h G).
32 #h #G #L #U #HU #b #f #K #HLK #T #HTU #n #T0 #H
33 elim (cpms_lifts_sn … H … HLK … HTU) -b -K #U0 #HTU0 #HU0
34 lapply (HU … HU0) -G -L /2 width=6 by teqw_inv_lifts_bi/
37 (* Advanced properties ******************************************************)
39 lemma cnuw_lref (h) (I) (G) (L):
40 ∀i. ❪G,L❫ ⊢ ➡𝐍𝐖*[h] #i → ❪G,L.ⓘ[I]❫ ⊢ ➡𝐍𝐖*[h] #↑i.
41 #h #I #G #L #i #Hi #n #X2 #H
42 elim (cpms_inv_lref_sn … H) -H *
45 lapply (Hi … HT2) -Hi -HT2 #H
46 lapply (teqw_inv_lref_sn … H) -H #H destruct
47 lapply (lifts_inv_lref1_uni … HTX2) -HTX2 #H destruct //
51 lemma cnuw_atom_drops (h) (b) (G) (L):
52 ∀i. ⇩*[b,𝐔❨i❩] L ≘ ⋆ → ❪G,L❫ ⊢ ➡𝐍𝐖*[h] #i.
53 #h #b #G #L #i #Hi #n #X #H
54 elim (cpms_inv_lref1_drops … H) -H * [ // || #m ] #K #V1 #V2 #HLK
55 lapply (drops_gen b … HLK) -HLK #HLK
56 lapply (drops_mono … Hi … HLK) -L #H destruct
59 lemma cnuw_unit_drops (h) (I) (G) (L):
60 ∀K,i. ⇩[i] L ≘ K.ⓤ[I] → ❪G,L❫ ⊢ ➡𝐍𝐖*[h] #i.
61 #h #I #G #L #K #i #HLK #n #X #H
62 elim (cpms_inv_lref1_drops … H) -H * [ // || #m ] #Y #V1 #V2 #HLY
63 lapply (drops_mono … HLK … HLY) -L #H destruct