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15 include "basic_2/computation/lsx_csx.ma".
16 include "basic_2/computation/fsb_alt.ma".
18 axiom fqup_lpxs_trans_nlleq: ∀h,g,G1,G2,K1,K2,T1,T2. ⦃G1, K1, T1⦄ ⊃+ ⦃G2, K2, T2⦄ →
19 ∀L2. ⦃G2, K2⦄ ⊢ ➡*[h, g] L2 → (K2 ⋕[T2, 0] L2 →⊥) →
20 ∃∃L1. ⦃G1, K1⦄ ⊢ ➡*[h, g] L1 &
21 K1 ⋕[T1, 0] L1 → ⊥ & ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄.
23 (* "BIG TREE" STRONGLY NORMALIZING TERMS ************************************)
25 (* Advanced propreties on context-senstive extended bormalizing terms *******)
27 lemma csx_fsb: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ ⦥[h, g] T.
28 #h #g #G1 #L1 #T1 #H @(csx_ind_alt … H) -T1
29 #T1 #HT1 @(csx_ind_lsx … (yinj 0) … HT1) -L1
30 #L1 @(fqup_wf_ind … G1 L1 T1) -G1 -L1 -T1
31 #G1 #L1 #T1 #IHu #H1 #IHl #IHc @fsb_intro
32 #G2 #L2 #T2 * -G2 -L2 -T2
33 [ #G2 #L2 #T2 #H12 @IHu -IHu // /2 width=5 by csx_fqup_conf/ -H1 [| -IHl ]
34 [ #L0 #HL20 #HnL20 #_ elim (fqup_lpxs_trans_nlleq … H12 … HL20 HnL20) -L2
35 /6 width=5 by fsb_fpbs_trans, lpxs_fpbs, fqup_fpbs, lpxs_cpxs_trans/
36 | #T0 #HT20 #HnT20 elim (fqup_cpxs_trans_neq … H12 … HT20 HnT20) -T2
37 /4 width=5 by fsb_fpbs_trans, fqup_fpbs/
39 | -H1 -IHu -IHl /3 width=1 by/
40 | -H1 -IHu /5 width=5 by fsb_fpbs_trans, lpxs_fpbs, lpxs_cpxs_trans/
44 (* Advanced eliminators *****************************************************)
46 lemma csx_ind_fpbu: ∀h,g. ∀R:relation3 genv lenv term.
47 (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
48 (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
51 ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → R G L T.
52 /4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_alt/ qed-.
54 lemma csx_ind_fpbg: ∀h,g. ∀R:relation3 genv lenv term.
55 (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
56 (∀G2,L2,T2. ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
59 ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → R G L T.
60 /4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_fpbg/ qed-.