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4 (* ||A|| A project by Andrea Asperti *)
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15 include "basic_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 UNCOUNTED PARALLEL RT-TRANSITION **********)
22 (* Main properties with atomic arity assignment *****************************)
24 theorem aaa_csx: ∀h,o,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
26 @(gcr_aaa … (csx_gcp h o) (csx_gcr h o) … H)
29 (* Advanced eliminators *****************************************************)
31 fact aaa_ind_csx_aux: ∀h,o,G,L,A. ∀R:predicate term.
32 (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
33 (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛[h, o] T2 → ⊥) → R T2) → R T1
35 ∀T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ T ⁝ A → R T.
36 #h #o #G #L #A #R #IH #T #H @(csx_ind … H) -T /4 width=5 by cpx_aaa_conf/
39 lemma aaa_ind_csx: ∀h,o,G,L,A. ∀R:predicate term.
40 (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
41 (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛[h, o] T2 → ⊥) → R T2) → R T1
43 ∀T. ⦃G, L⦄ ⊢ T ⁝ A → R T.
44 /5 width=9 by aaa_ind_csx_aux, aaa_csx/ qed-.
46 fact aaa_ind_csx_cpxs_aux: ∀h,o,G,L,A. ∀R:predicate term.
47 (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
48 (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛[h, o] T2 → ⊥) → R T2) → R T1
50 ∀T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ T ⁝ A → R T.
51 #h #o #G #L #A #R #IH #T #H @(csx_ind_cpxs … H) -T /4 width=5 by cpxs_aaa_conf/
54 (* Basic_2A1: was: aaa_ind_csx_alt *)
55 lemma aaa_ind_csx_cpxs: ∀h,o,G,L,A. ∀R:predicate term.
56 (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
57 (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛[h, o] T2 → ⊥) → R T2) → R T1
59 ∀T. ⦃G, L⦄ ⊢ T ⁝ A → R T.
60 /5 width=9 by aaa_ind_csx_cpxs_aux, aaa_csx/ qed-.