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14
15 include "basic_2/rt_computation/rsx_drops.ma".
16 include "basic_2/rt_computation/rsx_lpxs.ma".
17 include "basic_2/rt_computation/jsx.ma".
18
19 (* COMPATIBILITY OF STRONG NORMALIZATION FOR EXTENDED RT-TRANSITION *********)
20
21 (* Properties with strongly normalizing referred local environments *********)
22
23 (* Basic_2A1: uses: lsx_cpx_trans_lcosx *)
24 lemma rsx_cpx_trans_jsx (G):
25       ∀L0,T1,T2. ❨G,L0❩ ⊢ T1 ⬈ T2 →
26       ∀L. G ⊢ L0 ⊒ L → G ⊢ ⬈*𝐒[T1] L → G ⊢ ⬈*𝐒[T2] L.
27 #G #L0 #T1 #T2 #H @(cpx_ind … H) -G -L0 -T1 -T2
28 [ //
29 | //
30 | #I0 #G #K0 #V1 #V2 #W2 #_ #IH #HVW2 #L #HK0 #HL
31   elim (jsx_inv_pair_sn … HK0) -HK0 *
32   [ #K #HK0 #H destruct
33     /4 width=8 by rsx_lifts, rsx_fwd_pair, drops_refl, drops_drop/
34   | #K #HK0 #HV1 #H destruct
35     /4 width=8 by rsx_lifts, drops_refl, drops_drop/
36   ]
37 | #I0 #G #K0 #T #U #i #_ #IH #HTU #L #HK0 #HL
38   elim (jsx_fwd_bind_sn … HK0) -HK0 #I #K #HK0 #H destruct
39   /6 width=8 by rsx_inv_lifts, rsx_lifts, drops_refl, drops_drop/
40 | #p #I0 #G #L0 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L #HL0 #HL
41   elim (rsx_inv_bind_void … HL) -HL
42   /4 width=2 by jsx_pair, rsx_bind_void/
43 | #I0 #G #L0 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L #HL0 #HL
44   elim (rsx_inv_flat … HL) -HL /3 width=2 by rsx_flat/
45 | #G #L0 #V #U1 #T1 #T2 #HTU1 #_ #IHT12 #L #HL0 #HL
46   elim (rsx_inv_bind_void … HL) -HL #HV #HU1
47   /5 width=8 by rsx_inv_lifts, drops_refl, drops_drop/
48 | #G #L0 #V #T1 #T2 #_ #IHT12 #L #HL0 #HL
49   elim (rsx_inv_flat … HL) -HL /2 width=2 by/
50 | #G #L0 #V1 #V2 #T #_ #IHV12 #L #HL0 #HL
51   elim (rsx_inv_flat … HL) -HL /2 width=2 by/
52 | #p #G #L0 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L #HL0 #HL
53   elim (rsx_inv_flat … HL) -HL #HV1 #HL
54   elim (rsx_inv_bind_void … HL) -HL #HW1 #HT1
55   /4 width=2 by jsx_pair, rsx_bind_void, rsx_flat/
56 | #p #G #L0 #V1 #V2 #U2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #HVU2 #L #HL0 #HL
57   elim (rsx_inv_flat … HL) -HL #HV1 #HL
58   elim (rsx_inv_bind_void … HL) -HL #HW1 #HT1
59   /6 width=8 by jsx_pair, rsx_lifts, rsx_bind_void, rsx_flat, drops_refl, drops_drop/
60 ]
61 qed-.
62
63 (* Advanced properties of strongly normalizing referred local environments **)
64
65 (* Basic_2A1: uses: lsx_cpx_trans_O *)
66 lemma rsx_cpx_trans (G):
67       ∀L,T1,T2. ❨G,L❩ ⊢ T1 ⬈ T2 →
68       G ⊢ ⬈*𝐒[T1] L → G ⊢ ⬈*𝐒[T2] L.
69 /3 width=6 by rsx_cpx_trans_jsx, jsx_refl/ qed-.
70
71 lemma rsx_cpxs_trans (G):
72       ∀L,T1,T2. ❨G,L❩ ⊢ T1 ⬈* T2 →
73       G ⊢ ⬈*𝐒[T1] L → G ⊢ ⬈*𝐒[T2] L.
74 #G #L #T1 #T2 #H
75 @(cpxs_ind_dx ??????? H) -T1 //
76 /3 width=3 by rsx_cpx_trans/
77 qed-.