(**************************************************************************)
include "basic_2/notation/relations/predtysnstrong_5.ma".
-include "basic_2/static/lfdeq.ma".
+include "static_2/static/rdeq.ma".
include "basic_2/rt_transition/lpx.ma".
(* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
definition rdsx (h) (o) (G) (T): predicate lenv ≝
- SN … (lpx h G) (lfdeq h o T).
+ SN … (lpx h G) (rdeq h o T).
interpretation
"strong normalization for unbound context-sensitive parallel rt-transition on referred entries (local environment)"
(* Basic_2A1: uses: lsx_ind *)
lemma rdsx_ind (h) (o) (G) (T):
- ∀R:predicate lenv.
+ ∀Q:predicate lenv.
(∀L1. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
- (∀L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → (L1 ≛[h, o, T] L2 → ⊥) → R L2) →
- R L1
+ (∀L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → (L1 ≛[h, o, T] L2 → ⊥) → Q L2) →
+ Q L1
) →
- ∀L. G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄ → R L.
-#h #o #G #T #R #H0 #L1 #H elim H -L1
+ ∀L. G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄ → Q L.
+#h #o #G #T #Q #H0 #L1 #H elim H -L1
/5 width=1 by SN_intro/
qed-.
#h #o #G #I #L #V #T #H
@(rdsx_ind … H) -L #L1 #_ #IHL1
@rdsx_intro #L2 #HL12 #HnL12
-/4 width=3 by lfdeq_fwd_pair_sn/
+/4 width=3 by rdeq_fwd_pair_sn/
qed-.
(* Basic_2A1: uses: lsx_fwd_flat_dx *)
#h #o #G #I #L #V #T #H
@(rdsx_ind … H) -L #L1 #_ #IHL1
@rdsx_intro #L2 #HL12 #HnL12
-/4 width=3 by lfdeq_fwd_flat_dx/
+/4 width=3 by rdeq_fwd_flat_dx/
qed-.
fact rdsx_fwd_pair_aux (h) (o) (G): ∀L. G ⊢ ⬈*[h, o, #0] 𝐒⦃L⦄ →
∀I,K,V. L = K.ⓑ{I}V → G ⊢ ⬈*[h, o, V] 𝐒⦃K⦄.
#h #o #G #L #H
@(rdsx_ind … H) -L #L1 #_ #IH #I #K1 #V #H destruct
-/5 width=5 by lpx_pair, rdsx_intro, lfdeq_fwd_zero_pair/
+/5 width=5 by lpx_pair, rdsx_intro, rdeq_fwd_zero_pair/
qed-.
lemma rdsx_fwd_pair (h) (o) (G):