(* *)
(**************************************************************************)
-include "basic_2/static/gcp_aaa.ma".
+include "static_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".
-(* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
+(* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
(* Main properties with atomic arity assignment *****************************)
(* Advanced eliminators *****************************************************)
-fact aaa_ind_csx_aux: ∀h,o,G,L,A. ∀R:predicate term.
+fact aaa_ind_csx_aux: ∀h,o,G,L,A. ∀Q:predicate term.
(∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
- (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛[h, o] T2 → ⊥) → R T2) → R T1
+ (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛[h, o] T2 → ⊥) → Q T2) → Q 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 … H) -T /4 width=5 by cpx_aaa_conf/
+ ∀T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ T ⁝ A → Q T.
+#h #o #G #L #A #Q #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.
+lemma aaa_ind_csx: ∀h,o,G,L,A. ∀Q:predicate term.
(∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
- (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛[h, o] T2 → ⊥) → R T2) → R T1
+ (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛[h, o] T2 → ⊥) → Q T2) → Q T1
) →
- ∀T. ⦃G, L⦄ ⊢ T ⁝ A → R T.
+ ∀T. ⦃G, L⦄ ⊢ T ⁝ A → Q T.
/5 width=9 by aaa_ind_csx_aux, aaa_csx/ qed-.
-fact aaa_ind_csx_cpxs_aux: ∀h,o,G,L,A. ∀R:predicate term.
+fact aaa_ind_csx_cpxs_aux: ∀h,o,G,L,A. ∀Q:predicate term.
(∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
- (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛[h, o] T2 → ⊥) → R T2) → R T1
+ (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛[h, o] T2 → ⊥) → Q T2) → Q 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/
+ ∀T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ T ⁝ A → Q T.
+#h #o #G #L #A #Q #IH #T #H @(csx_ind_cpxs … H) -T /4 width=5 by cpxs_aaa_conf/
qed-.
(* Basic_2A1: was: aaa_ind_csx_alt *)
-lemma aaa_ind_csx_cpxs: ∀h,o,G,L,A. ∀R:predicate term.
+lemma aaa_ind_csx_cpxs: ∀h,o,G,L,A. ∀Q:predicate term.
(∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
- (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛[h, o] T2 → ⊥) → R T2) → R T1
+ (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛[h, o] T2 → ⊥) → Q T2) → Q T1
) →
- ∀T. ⦃G, L⦄ ⊢ T ⁝ A → R T.
+ ∀T. ⦃G, L⦄ ⊢ T ⁝ A → Q T.
/5 width=9 by aaa_ind_csx_cpxs_aux, aaa_csx/ qed-.