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4 (* ||A|| A project by Andrea Asperti *)
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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".
20 (* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
22 (* Main properties with atomic arity assignment *****************************)
24 theorem aaa_csx (h) (G) (L):
25 ∀T,A. ❪G,L❫ ⊢ T ⁝ A → ❪G,L❫ ⊢ ⬈*𝐒[h] T.
27 @(gcr_aaa … (csx_gcp h) (csx_gcr h) … H)
30 (* Advanced eliminators *****************************************************)
32 fact aaa_ind_csx_aux (h) (G) (L):
33 ∀A. ∀Q:predicate term.
34 (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
35 (∀T2. ❪G,L❫ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
37 ∀T. ❪G,L❫ ⊢ ⬈*𝐒[h] T → ❪G,L❫ ⊢ T ⁝ A → Q T.
38 #h #G #L #A #Q #IH #T #H @(csx_ind … H) -T /4 width=5 by cpx_aaa_conf/
41 lemma aaa_ind_csx (h) (G) (L):
42 ∀A. ∀Q:predicate term.
43 (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
44 (∀T2. ❪G,L❫ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
46 ∀T. ❪G,L❫ ⊢ T ⁝ A → Q T.
47 /5 width=9 by aaa_ind_csx_aux, aaa_csx/ qed-.
49 fact aaa_ind_csx_cpxs_aux (h) (G) (L):
50 ∀A. ∀Q:predicate term.
51 (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
52 (∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
54 ∀T. ❪G,L❫ ⊢ ⬈*𝐒[h] T → ❪G,L❫ ⊢ T ⁝ A → Q T.
55 #h #G #L #A #Q #IH #T #H @(csx_ind_cpxs … H) -T /4 width=5 by cpxs_aaa_conf/
58 (* Basic_2A1: was: aaa_ind_csx_alt *)
59 lemma aaa_ind_csx_cpxs (h) (G) (L):
60 ∀A. ∀Q:predicate term.
61 (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
62 (∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
64 ∀T. ❪G,L❫ ⊢ T ⁝ A → Q T.
65 /5 width=9 by aaa_ind_csx_cpxs_aux, aaa_csx/ qed-.