+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/computation/gcp_aaa.ma".
-include "basic_2/computation/cpxs_aaa.ma".
-include "basic_2/computation/csx_theq_vector.ma".
-
-(* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERMS ********************)
-
-(* Main properties on atomic arity assignment *******************************)
-
-theorem aaa_csx: ∀h,o,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦃G, L⦄ ⊢ ⬊*[h, o] T.
-#h #o #G #L #T #A #H
-@(gcr_aaa … (csx_gcp h o) (csx_gcr h o) … H)
-qed.
-
-(* Advanced eliminators *****************************************************)
-
-fact aaa_ind_csx_aux: ∀h,o,G,L,A. ∀R:predicate term.
- (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
- (∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, o] T2 → (T1 = T2 → ⊥) → R T2) → R T1
- ) →
- ∀T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → ⦃G, L⦄ ⊢ T ⁝ A → R T.
-#h #o #G #L #A #R #IH #T #H @(csx_ind … H) -T /4 width=5 by cpx_aaa_conf/
-qed-.
-
-lemma aaa_ind_csx: ∀h,o,G,L,A. ∀R:predicate term.
- (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
- (∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, o] 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,o,G,L,A. ∀R:predicate term.
- (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
- (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2 → (T1 = T2 → ⊥) → R T2) → R T1
- ) →
- ∀T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → ⦃G, L⦄ ⊢ T ⁝ A → R T.
-#h #o #G #L #A #R #IH #T #H @(csx_ind_alt … H) -T /4 width=5 by cpxs_aaa_conf/
-qed-.
-
-lemma aaa_ind_csx_alt: ∀h,o,G,L,A. ∀R:predicate term.
- (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
- (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, o] 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-.