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14
15 include "static_2/static/gcp_aaa.ma".
16 include "basic_2/rt_computation/cpxs_aaa.ma".
17 include "basic_2/rt_computation/csx_gcp.ma".
18 include "basic_2/rt_computation/csx_gcr.ma".
19
20 (* STRONGLY NORMALIZING TERMS FOR EXTENDED PARALLEL RT-TRANSITION ***********)
21
22 (* Main properties with atomic arity assignment *****************************)
23
24 theorem aaa_csx (G) (L):
25         ∀T,A. ❪G,L❫ ⊢ T ⁝ A → ❪G,L❫ ⊢ ⬈*𝐒 T.
26 #G #L #T #A #H
27 @(gcr_aaa … csx_gcp csx_gcr … H)
28 qed.
29
30 (* Advanced eliminators *****************************************************)
31
32 fact aaa_ind_csx_aux (G) (L):
33      ∀A. ∀Q:predicate ….
34      (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
35        (∀T2. ❪G,L❫ ⊢ T1 ⬈ T2 → (T1 ≅ T2 → ⊥) → Q T2) → Q T1
36      ) →
37      ∀T. ❪G,L❫ ⊢ ⬈*𝐒 T → ❪G,L❫ ⊢ T ⁝ A →  Q T.
38 #G #L #A #Q #IH #T #H @(csx_ind … H) -T /4 width=5 by cpx_aaa_conf/
39 qed-.
40
41 lemma aaa_ind_csx (G) (L):
42       ∀A. ∀Q:predicate ….
43       (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
44         (∀T2. ❪G,L❫ ⊢ T1 ⬈ T2 → (T1 ≅ T2 → ⊥) → Q T2) → Q T1
45       ) →
46       ∀T. ❪G,L❫ ⊢ T ⁝ A → Q T.
47 /5 width=9 by aaa_ind_csx_aux, aaa_csx/ qed-.
48
49 fact aaa_ind_csx_cpxs_aux (G) (L):
50      ∀A. ∀Q:predicate ….
51      (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
52        (∀T2. ❪G,L❫ ⊢ T1 ⬈* T2 → (T1 ≅ T2 → ⊥) → Q T2) → Q T1
53      ) →
54      ∀T. ❪G,L❫ ⊢ ⬈*𝐒 T → ❪G,L❫ ⊢ T ⁝ A →  Q T.
55 #G #L #A #Q #IH #T #H @(csx_ind_cpxs … H) -T /4 width=5 by cpxs_aaa_conf/
56 qed-.
57
58 (* Basic_2A1: was: aaa_ind_csx_alt *)
59 lemma aaa_ind_csx_cpxs (G) (L):
60       ∀A. ∀Q:predicate ….
61       (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
62         (∀T2. ❪G,L❫ ⊢ T1 ⬈* T2 → (T1 ≅ T2 → ⊥) → Q T2) → Q T1
63       ) →
64       ∀T. ❪G,L❫ ⊢ T ⁝ A → Q T.
65 /5 width=9 by aaa_ind_csx_cpxs_aux, aaa_csx/ qed-.