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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/computation/acp_aaa.ma".
16 include "basic_2/computation/cpxs_aaa.ma".
17 include "basic_2/computation/csx_tstc_vector.ma".
19 (* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERMS ********************)
21 (* Main properties on atomic arity assignment *******************************)
23 theorem aaa_csx: ∀h,g,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
25 @(acp_aaa … (csx_acp h g) (csx_acr h g) … H)
28 (* Advanced eliminators *****************************************************)
30 fact aaa_ind_csx_aux: ∀h,g,G,L,A. ∀R:predicate term.
31 (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
32 (∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
34 ∀T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ T ⁝ A → R T.
35 #h #g #G #L #A #R #IH #T #H @(csx_ind … H) -T /4 width=5 by aaa_cpx_conf/
38 lemma aaa_ind_csx: ∀h,g,G,L,A. ∀R:predicate term.
39 (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
40 (∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
42 ∀T. ⦃G, L⦄ ⊢ T ⁝ A → R T.
43 /5 width=9 by aaa_ind_csx_aux, aaa_csx/ qed-.
45 fact aaa_ind_csx_alt_aux: ∀h,g,G,L,A. ∀R:predicate term.
46 (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
47 (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
49 ∀T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ T ⁝ A → R T.
50 #h #g #G #L #A #R #IH #T #H @(csx_ind_alt … H) -T /4 width=5 by aaa_cpxs_conf/
53 lemma aaa_ind_csx_alt: ∀h,g,G,L,A. ∀R:predicate term.
54 (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
55 (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
57 ∀T. ⦃G, L⦄ ⊢ T ⁝ A → R T.
58 /5 width=9 by aaa_ind_csx_alt_aux, aaa_csx/ qed-.