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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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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 *******************)
25 ∀G,L,T,A. ❪G,L❫ ⊢ T ⁝ A → ≥𝐒 ❪G,L,T❫.
26 /3 width=2 by aaa_csx, csx_fsb/ qed.
28 (* Advanced eliminators with atomic arity assignment for terms **************)
30 fact aaa_ind_fpb_aux (Q:relation3 …):
33 (∀G2,L2,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ → Q G2 L2 T2) →
36 ∀G,L,T. ❪G,L❫ ⊢ ⬈*𝐒 T → ∀A. ❪G,L❫ ⊢ T ⁝ A → Q G L T.
37 #R #IH #G #L #T #H @(csx_ind_fpb … H) -G -L -T
38 #G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
39 #G2 #L2 #T2 #H12 elim (fpbs_aaa_conf … G2 … L2 … T2 … HTA1) -A1
40 /2 width=2 by fpb_fpbs/
43 lemma aaa_ind_fpb (Q:relation3 …):
46 (∀G2,L2,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ → Q G2 L2 T2) →
49 ∀G,L,T,A. ❪G,L❫ ⊢ T ⁝ A → Q G L T.
50 /4 width=4 by aaa_ind_fpb_aux, aaa_csx/ qed-.
52 fact aaa_ind_fpbg_aux (Q:relation3 …):
55 (∀G2,L2,T2. ❪G1,L1,T1❫ > ❪G2,L2,T2❫ → Q G2 L2 T2) →
58 ∀G,L,T. ❪G,L❫ ⊢ ⬈*𝐒 T → ∀A. ❪G,L❫ ⊢ T ⁝ A → Q G L T.
59 #Q #IH #G #L #T #H @(csx_ind_fpbg … H) -G -L -T
60 #G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
61 #G2 #L2 #T2 #H12 elim (fpbs_aaa_conf … G2 … L2 … T2 … HTA1) -A1
62 /2 width=2 by fpbg_fwd_fpbs/
65 lemma aaa_ind_fpbg (Q:relation3 …):
68 (∀G2,L2,T2. ❪G1,L1,T1❫ > ❪G2,L2,T2❫ → Q G2 L2 T2) →
71 ∀G,L,T,A. ❪G,L❫ ⊢ T ⁝ A → Q G L T.
72 /4 width=4 by aaa_ind_fpbg_aux, aaa_csx/ qed-.