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/rdeq_drops.ma".
16 include "basic_2/rt_transition/lpx_drops.ma".
17 include "basic_2/rt_computation/rdsx_length.ma".
18 include "basic_2/rt_computation/rdsx_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 rdsx_lifts (h) (o) (G): d_liftable1_isuni … (λL,T. G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄).
27 #h #o #G #K #T #H @(rdsx_ind … H) -K
28 #K1 #_ #IH #b #f #L1 #HLK1 #Hf #U #HTU @rdsx_intro
29 #L2 #HL12 #HnL12 elim (lpx_drops_conf … HLK1 … HL12)
30 /5 width=9 by rdeq_lifts_bi, lpx_fwd_length/
33 (* Inversion lemmas on relocation *******************************************)
35 (* Basic_2A1: uses: lsx_inv_lift_le lsx_inv_lift_be lsx_inv_lift_ge *)
36 lemma rdsx_inv_lifts (h) (o) (G): d_deliftable1_isuni … (λL,T. G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄).
37 #h #o #G #L #U #H @(rdsx_ind … H) -L
38 #L1 #_ #IH #b #f #K1 #HLK1 #Hf #T #HTU @rdsx_intro
39 #K2 #HK12 #HnK12 elim (drops_lpx_trans … HLK1 … HK12) -HK12
40 /4 width=10 by rdeq_inv_lifts_bi/
43 (* Advanced properties ******************************************************)
45 (* Basic_2A1: uses: lsx_lref_free *)
46 lemma rdsx_lref_atom (h) (o) (G): ∀L,i. ⬇*[Ⓕ, 𝐔❴i❵] L ≘ ⋆ → G ⊢ ⬈*[h, o, #i] 𝐒⦃L⦄.
48 @(rdsx_lifts … (#0) … HL1) -HL1 //
51 (* Basic_2A1: uses: lsx_lref_skip *)
52 lemma rdsx_lref_unit (h) (o) (G): ∀I,L,K,i. ⬇*[i] L ≘ K.ⓤ{I} → G ⊢ ⬈*[h, o, #i] 𝐒⦃L⦄.
53 #h #o #G #I #L1 #K1 #i #HL1
54 @(rdsx_lifts … (#0) … HL1) -HL1 //
57 (* Advanced forward lemmas **************************************************)
59 (* Basic_2A1: uses: lsx_fwd_lref_be *)
60 lemma rdsx_fwd_lref_pair (h) (o) (G):
61 ∀L,i. G ⊢ ⬈*[h, o, #i] 𝐒⦃L⦄ →
62 ∀I,K,V. ⬇*[i] L ≘ K.ⓑ{I}V → G ⊢ ⬈*[h, o, V] 𝐒⦃K⦄.
63 #h #o #G #L #i #HL #I #K #V #HLK
64 lapply (rdsx_inv_lifts … HL … HLK … (#0) ?) -L
65 /2 width=2 by rdsx_fwd_pair/