(**************************************************************************)
include "basic_2/computation/acp_aaa.ma".
+include "basic_2/computation/cpxs_aaa.ma".
include "basic_2/computation/csx_tstc_vector.ma".
(* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERMS ********************)
#h #g #G #L #T #A #H
@(acp_aaa … (csx_acp h g) (csx_acr h g) … H)
qed.
+
+(* Advanced eliminators *****************************************************)
+
+fact aaa_ind_csx_aux: ∀h,g,G,L,A. ∀R:predicate term.
+ (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
+ (∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
+ ) →
+ ∀T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ T ⁝ A → R T.
+#h #g #G #L #A #R #IH #T #H @(csx_ind … H) -T /4 width=5 by aaa_cpx_conf/
+qed-.
+
+lemma aaa_ind_csx: ∀h,g,G,L,A. ∀R:predicate term.
+ (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
+ (∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
+ ) →
+ ∀T. ⦃G, L⦄ ⊢ T ⁝ A → R T.
+/5 width=9 by aaa_ind_csx_aux, aaa_csx/ qed-.
+
+fact aaa_ind_csx_alt_aux: ∀h,g,G,L,A. ∀R:predicate term.
+ (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
+ (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
+ ) →
+ ∀T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ T ⁝ A → R T.
+#h #g #G #L #A #R #IH #T #H @(csx_ind_alt … H) -T /4 width=5 by aaa_cpxs_conf/
+qed-.
+
+lemma aaa_ind_csx_alt: ∀h,g,G,L,A. ∀R:predicate term.
+ (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
+ (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
+ ) →
+ ∀T. ⦃G, L⦄ ⊢ T ⁝ A → R T.
+/5 width=9 by aaa_ind_csx_alt_aux, aaa_csx/ qed-.