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/rt_computation/rdsx_drops.ma".
16 include "basic_2/rt_computation/rdsx_lpxs.ma".
17 include "basic_2/rt_computation/lsubsx.ma".
19 (* CLEAR OF STRONGLY NORMALIZING ENTRIES FOR UNBOUND RT-TRANSITION **********)
21 (* Properties with strongly normalizing referred local environments *********)
23 (* Basic_2A1: uses: lsx_cpx_trans_lcosx *)
24 lemma rdsx_cpx_trans_lsubsx (h):
25 ∀G,L0,T1,T2. ⦃G,L0⦄ ⊢ T1 ⬈[h] T2 →
26 ∀f,L. G ⊢ L0 ⊆ⓧ[h,f] L →
27 G ⊢ ⬈*[h,T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h,T2] 𝐒⦃L⦄.
28 #h #G #L0 #T1 #T2 #H @(cpx_ind … H) -G -L0 -T1 -T2 //
29 [ #I0 #G #K0 #V1 #V2 #W2 #_ #IH #HVW2 #g #L #HK0 #HL
30 elim (lsubsx_inv_pair_sn_gen … HK0) -HK0 *
31 [ #f #K #HK0 #H1 #H2 destruct
32 /4 width=8 by rdsx_lifts, rdsx_fwd_pair, drops_refl, drops_drop/
33 | #f #K #HV1 #HK0 #H1 #H2 destruct
34 /4 width=8 by rdsx_lifts, drops_refl, drops_drop/
36 | #I0 #G #K0 #T #U #i #_ #IH #HTU #g #L #HK0 #HL
37 elim (lsubsx_fwd_bind_sn … HK0) -HK0 #I #K #HK0 #H destruct
38 /6 width=8 by rdsx_inv_lifts, rdsx_lifts, drops_refl, drops_drop/
39 | #p #I0 #G #L0 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #f #L #HL0 #HL
40 elim (rdsx_inv_bind … HL) -HL
41 /4 width=2 by lsubsx_pair, rdsx_bind_void/
42 | #I0 #G #L0 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #f #L #HL0 #HL
43 elim (rdsx_inv_flat … HL) -HL /3 width=2 by rdsx_flat/
44 | #G #L0 #V #U1 #T1 #T2 #HTU1 #_ #IHT12 #f #L #HL0 #HL
45 elim (rdsx_inv_bind … HL) -HL #HV #HU1
46 /5 width=8 by rdsx_inv_lifts, drops_refl, drops_drop/
47 | #G #L0 #V #T1 #T2 #_ #IHT12 #f #L #HL0 #HL
48 elim (rdsx_inv_flat … HL) -HL /2 width=2 by/
49 | #G #L0 #V1 #V2 #T #_ #IHV12 #f #L #HL0 #HL
50 elim (rdsx_inv_flat … HL) -HL /2 width=2 by/
51 | #p #G #L0 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #f #L #HL0 #HL
52 elim (rdsx_inv_flat … HL) -HL #HV1 #HL
53 elim (rdsx_inv_bind … HL) -HL #HW1 #HT1
54 /4 width=2 by lsubsx_pair, rdsx_bind_void, rdsx_flat/
55 | #p #G #L0 #V1 #V2 #U2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #HVU2 #f #L #HL0 #HL
56 elim (rdsx_inv_flat … HL) -HL #HV1 #HL
57 elim (rdsx_inv_bind … HL) -HL #HW1 #HT1
58 /6 width=8 by lsubsx_pair, rdsx_lifts, rdsx_bind_void, rdsx_flat, drops_refl, drops_drop/
62 (* Advanced properties of strongly normalizing referred local environments **)
64 (* Basic_2A1: uses: lsx_cpx_trans_O *)
65 lemma rdsx_cpx_trans (h):
66 ∀G,L,T1,T2. ⦃G,L⦄ ⊢ T1 ⬈[h] T2 →
67 G ⊢ ⬈*[h,T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h,T2] 𝐒⦃L⦄.
68 /3 width=6 by rdsx_cpx_trans_lsubsx, lsubsx_refl/ qed-.
70 lemma rdsx_cpxs_trans (h):
71 ∀G,L,T1,T2. ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 →
72 G ⊢ ⬈*[h,T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h,T2] 𝐒⦃L⦄.
74 @(cpxs_ind_dx ???????? H) -T1 //
75 /3 width=3 by rdsx_cpx_trans/