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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/fsb_csx.ma".
19 (* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
21 (* Main properties with atomic arity assignment for terms *******************)
23 theorem aaa_fsb (G) (L) (T) (A):
24 ❨G,L❩ ⊢ T ⁝ A → ≥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_fpbc_aux (Q:relation3 …):
32 (∀G2,L2,T2. ❨G1,L1,T1❩ ≻ ❨G2,L2,T2❩ → Q G2 L2 T2) →
35 ∀G,L,T. ❨G,L❩ ⊢ ⬈*𝐒 T → ∀A. ❨G,L❩ ⊢ T ⁝ A → Q G L T.
36 #R #IH #G #L #T #H @(csx_ind_fpbc … H) -G -L -T
37 #G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
38 #G2 #L2 #T2 #H12 elim (fpbs_aaa_conf … G2 … L2 … T2 … HTA1) -A1
39 /2 width=2 by fpbc_fpbs/
42 lemma aaa_ind_fpbc (Q:relation3 …):
45 (∀G2,L2,T2. ❨G1,L1,T1❩ ≻ ❨G2,L2,T2❩ → Q G2 L2 T2) →
48 ∀G,L,T,A. ❨G,L❩ ⊢ T ⁝ A → Q G L T.
49 /4 width=4 by aaa_ind_fpbc_aux, aaa_csx/ qed-.
51 fact aaa_ind_fpbg_aux (Q:relation3 …):
54 (∀G2,L2,T2. ❨G1,L1,T1❩ > ❨G2,L2,T2❩ → Q G2 L2 T2) →
57 ∀G,L,T. ❨G,L❩ ⊢ ⬈*𝐒 T → ∀A. ❨G,L❩ ⊢ T ⁝ A → Q G L T.
58 #Q #IH #G #L #T #H @(csx_ind_fpbg … H) -G -L -T
59 #G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
60 #G2 #L2 #T2 #H12 elim (fpbs_aaa_conf … G2 … L2 … T2 … HTA1) -A1
61 /2 width=2 by fpbg_fwd_fpbs/
64 lemma aaa_ind_fpbg (Q:relation3 …):
67 (∀G2,L2,T2. ❨G1,L1,T1❩ > ❨G2,L2,T2❩ → Q G2 L2 T2) →
70 ∀G,L,T,A. ❨G,L❩ ⊢ T ⁝ A → Q G L T.
71 /4 width=4 by aaa_ind_fpbg_aux, aaa_csx/ qed-.