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/static/reqx_drops.ma".
16 include "basic_2/rt_transition/lpx_drops.ma".
17 include "basic_2/rt_computation/rsx_length.ma".
18 include "basic_2/rt_computation/rsx_fqup.ma".
20 (* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
22 (* Properties with generic relocation ***************************************)
24 (* Note: this uses length *)
25 (* Basic_2A1: uses: lsx_lift_le lsx_lift_ge *)
26 lemma rsx_lifts (h) (G):
27 d_liftable1_isuni … (λL,T. G ⊢ ⬈*𝐒[h,T] L).
28 #h #G #K #T #H @(rsx_ind … H) -K
29 #K1 #_ #IH #b #f #L1 #HLK1 #Hf #U #HTU @rsx_intro
30 #L2 #HL12 #HnL12 elim (lpx_drops_conf … HLK1 … HL12)
31 /5 width=9 by reqx_lifts_bi, lpx_fwd_length/
34 (* Inversion lemmas on relocation *******************************************)
36 (* Basic_2A1: uses: lsx_inv_lift_le lsx_inv_lift_be lsx_inv_lift_ge *)
37 lemma rsx_inv_lifts (h) (G):
38 d_deliftable1_isuni … (λL,T. G ⊢ ⬈*𝐒[h,T] L).
39 #h #G #L #U #H @(rsx_ind … H) -L
40 #L1 #_ #IH #b #f #K1 #HLK1 #Hf #T #HTU @rsx_intro
41 #K2 #HK12 #HnK12 elim (drops_lpx_trans … HLK1 … HK12) -HK12
42 /4 width=10 by reqx_inv_lifts_bi/
45 (* Advanced properties ******************************************************)
47 (* Basic_2A1: uses: lsx_lref_free *)
48 lemma rsx_lref_atom_drops (h) (G):
49 ∀L,i. ⇩*[Ⓕ,𝐔❨i❩] L ≘ ⋆ → G ⊢ ⬈*𝐒[h,#i] L.
51 @(rsx_lifts … (#0) … HL1) -HL1 //
54 (* Basic_2A1: uses: lsx_lref_skip *)
55 lemma rsx_lref_unit_drops (h) (G):
56 ∀I,L,K,i. ⇩[i] L ≘ K.ⓤ[I] → G ⊢ ⬈*𝐒[h,#i] L.
57 #h #G #I #L1 #K1 #i #HL1
58 @(rsx_lifts … (#0) … HL1) -HL1 //
61 (* Advanced forward lemmas **************************************************)
63 (* Basic_2A1: uses: lsx_fwd_lref_be *)
64 lemma rsx_fwd_lref_pair_drops (h) (G):
65 ∀L,i. G ⊢ ⬈*𝐒[h,#i] L →
66 ∀I,K,V. ⇩[i] L ≘ K.ⓑ[I]V → G ⊢ ⬈*𝐒[h,V] K.
67 #h #G #L #i #HL #I #K #V #HLK
68 lapply (rsx_inv_lifts … HL … HLK … (#0) ?) -L
69 /2 width=2 by rsx_fwd_pair/