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4 (* ||A|| A project by Andrea Asperti *)
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15 include "basic_2/rt_computation/csx_aaa.ma".
16 include "basic_2/rt_computation/fpbs_aaa.ma".
17 include "basic_2/rt_computation/fpbs_fpb.ma".
18 include "basic_2/rt_computation/fsb_csx.ma".
20 (* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
22 (* Main properties with atomic arity assignment for terms *******************)
24 theorem aaa_fsb: ∀h,G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → ≥[h] 𝐒⦃G,L,T⦄.
25 /3 width=2 by aaa_csx, csx_fsb/ qed.
27 (* Advanced eliminators with atomic arity assignment for terms **************)
29 fact aaa_ind_fpb_aux: ∀h. ∀Q:relation3 ….
30 (∀G1,L1,T1,A. ⦃G1,L1⦄ ⊢ T1 ⁝ A →
31 (∀G2,L2,T2. ⦃G1,L1,T1⦄ ≻[h] ⦃G2,L2,T2⦄ → Q G2 L2 T2) →
34 ∀G,L,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ∀A. ⦃G,L⦄ ⊢ T ⁝ A → Q G L T.
35 #h #R #IH #G #L #T #H @(csx_ind_fpb … H) -G -L -T
36 #G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
37 #G2 #L2 #T2 #H12 elim (fpbs_aaa_conf … G2 … L2 … T2 … HTA1) -A1
38 /2 width=2 by fpb_fpbs/
41 lemma aaa_ind_fpb: ∀h. ∀Q:relation3 ….
42 (∀G1,L1,T1,A. ⦃G1,L1⦄ ⊢ T1 ⁝ A →
43 (∀G2,L2,T2. ⦃G1,L1,T1⦄ ≻[h] ⦃G2,L2,T2⦄ → Q G2 L2 T2) →
46 ∀G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → Q G L T.
47 /4 width=4 by aaa_ind_fpb_aux, aaa_csx/ qed-.
49 fact aaa_ind_fpbg_aux: ∀h. ∀Q:relation3 ….
50 (∀G1,L1,T1,A. ⦃G1,L1⦄ ⊢ T1 ⁝ A →
51 (∀G2,L2,T2. ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄ → Q G2 L2 T2) →
54 ∀G,L,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ∀A. ⦃G,L⦄ ⊢ T ⁝ A → Q G L T.
55 #h #Q #IH #G #L #T #H @(csx_ind_fpbg … H) -G -L -T
56 #G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
57 #G2 #L2 #T2 #H12 elim (fpbs_aaa_conf … G2 … L2 … T2 … HTA1) -A1
58 /2 width=2 by fpbg_fwd_fpbs/
61 lemma aaa_ind_fpbg: ∀h. ∀Q:relation3 ….
62 (∀G1,L1,T1,A. ⦃G1,L1⦄ ⊢ T1 ⁝ A →
63 (∀G2,L2,T2. ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄ → Q G2 L2 T2) →
66 ∀G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → Q G L T.
67 /4 width=4 by aaa_ind_fpbg_aux, aaa_csx/ qed-.