(* *)
(**************************************************************************)
-include "basic_2/computation/gcp_aaa.ma".
-include "basic_2/computation/cpxs_aaa.ma".
-include "basic_2/computation/csx_theq_vector.ma".
+include "basic_2/static/gcp_aaa.ma".
+include "basic_2/rt_computation/cpxs_aaa.ma".
+include "basic_2/rt_computation/csx_gcp.ma".
+include "basic_2/rt_computation/csx_gcr.ma".
-(* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERMS ********************)
+(* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
-(* Main properties on atomic arity assignment *******************************)
+(* Main properties with atomic arity assignment *****************************)
-theorem aaa_csx: â\88\80h,o,G,L,T,A. â¦\83G, Lâ¦\84 â\8a¢ T â\81\9d A â\86\92 â¦\83G, Lâ¦\84 â\8a¢ â¬\8a*[h, o] T.
+theorem aaa_csx: â\88\80h,o,G,L,T,A. â¦\83G, Lâ¦\84 â\8a¢ T â\81\9d A â\86\92 â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, o] ð\9d\90\92â¦\83Tâ¦\84.
#h #o #G #L #T #A #H
@(gcr_aaa … (csx_gcp h o) (csx_gcr h o) … H)
qed.
fact aaa_ind_csx_aux: ∀h,o,G,L,A. ∀R:predicate term.
(∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
- (â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡[h, o] T2 â\86\92 (T1 = T2 → ⊥) → R T2) → R T1
+ (â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88[h] T2 â\86\92 (T1 â\89\9b[h, o] T2 → ⊥) → R T2) → R T1
) →
- â\88\80T. â¦\83G, Lâ¦\84 â\8a¢ â¬\8a*[h, o] T → ⦃G, L⦄ ⊢ T ⁝ A → R T.
+ â\88\80T. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, o] ð\9d\90\92â¦\83Tâ¦\84 → ⦃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 →
- (â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡[h, o] T2 â\86\92 (T1 = T2 → ⊥) → R T2) → R T1
+ (â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88[h] T2 â\86\92 (T1 â\89\9b[h, o] 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/
+fact aaa_ind_csx_cpxs_aux: ∀h,o,G,L,A. ∀R:predicate term.
+ (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
+ (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛[h, o] T2 → ⊥) → R T2) → R T1
+ ) →
+ ∀T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ T ⁝ A → R T.
+#h #o #G #L #A #R #IH #T #H @(csx_ind_cpxs … 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-.
+(* Basic_2A1: was: aaa_ind_csx_alt *)
+lemma aaa_ind_csx_cpxs: ∀h,o,G,L,A. ∀R:predicate term.
+ (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
+ (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛[h, o] T2 → ⊥) → R T2) → R T1
+ ) →
+ ∀T. ⦃G, L⦄ ⊢ T ⁝ A → R T.
+/5 width=9 by aaa_ind_csx_cpxs_aux, aaa_csx/ qed-.