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15 include "basic_2/rt_computation/lfsx_drops.ma".
16 include "basic_2/rt_computation/lfsx_lfpxs.ma".
17 include "basic_2/rt_computation/lsubsx.ma".
19 (* CLEAR OF STRONGLY NORMALIZING ENTRIES FOR UNCOUNTED RT-TRANSITION ********)
21 (* Properties with strong normalizing env's for uncounted rt-transition *****)
23 (* Basic_2A1: uses: lsx_cpx_trans_lcosx *)
24 lemma lfsx_cpx_trans_lsubsx: ∀h,o,G,L0,T1,T2. ⦃G, L0⦄ ⊢ T1 ⬈[h] T2 →
25 ∀f,L. G ⊢ L0 ⊆ⓧ[h, o, f] L →
26 G ⊢ ⬈*[h, o, T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h, o, T2] 𝐒⦃L⦄.
27 #h #o #G #L0 #T1 #T2 #H @(cpx_ind … H) -G -L0 -T1 -T2 //
28 [ #I0 #G #K0 #V1 #V2 #W2 #_ #IH #HVW2 #g #L #HK0 #HL
29 elim (lsubsx_inv_pair_sn_gen … HK0) -HK0 *
30 [ #f #K #HK0 #H1 #H2 destruct
31 /4 width=8 by lfsx_lifts, lfsx_fwd_pair, drops_refl, drops_drop/
32 | #f #K #HV1 #HK0 #H1 #H2 destruct
33 /4 width=8 by lfsx_lifts, drops_refl, drops_drop/
35 | #I0 #G #K0 #T #U #i #_ #IH #HTU #g #L #HK0 #HL
36 elim (lsubsx_fwd_bind_sn … HK0) -HK0 #I #K #HK0 #H destruct
37 /6 width=8 by lfsx_inv_lifts, lfsx_lifts, drops_refl, drops_drop/
38 | #p #I0 #G #L0 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #f #L #HL0 #HL
39 elim (lfsx_inv_bind … HL) -HL
40 /4 width=2 by lsubsx_pair, lfsx_bind_void/
41 | #I0 #G #L0 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #f #L #HL0 #HL
42 elim (lfsx_inv_flat … HL) -HL /3 width=2 by lfsx_flat/
43 | #G #L0 #V #U1 #U2 #T2 #_ #HTU2 #IHU12 #f #L #HL0 #HL
44 elim (lfsx_inv_bind … HL) -HL #HV #HU1
45 /4 width=8 by lsubsx_pair, lfsx_inv_lifts, drops_refl, drops_drop/
46 | #G #L0 #V #T1 #T2 #_ #IHT12 #f #L #HL0 #HL
47 elim (lfsx_inv_flat … HL) -HL /2 width=2 by/
48 | #G #L0 #V1 #V2 #T #_ #IHV12 #f #L #HL0 #HL
49 elim (lfsx_inv_flat … HL) -HL /2 width=2 by/
50 | #p #G #L0 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #f #L #HL0 #HL
51 elim (lfsx_inv_flat … HL) -HL #HV1 #HL
52 elim (lfsx_inv_bind … HL) -HL #HW1 #HT1
53 /4 width=2 by lsubsx_pair, lfsx_bind_void, lfsx_flat/
54 | #p #G #L0 #V1 #V2 #U2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #HVU2 #f #L #HL0 #HL
55 elim (lfsx_inv_flat … HL) -HL #HV1 #HL
56 elim (lfsx_inv_bind … HL) -HL #HW1 #HT1
57 /6 width=8 by lsubsx_pair, lfsx_lifts, lfsx_bind_void, lfsx_flat, drops_refl, drops_drop/
61 (* Basic_2A1: uses: lsx_cpx_trans_O *)
62 lemma lfsx_cpx_trans: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 →
63 G ⊢ ⬈*[h, o, T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h, o, T2] 𝐒⦃L⦄.
64 /3 width=6 by lfsx_cpx_trans_lsubsx, lsubsx_refl/ qed-.