milestone in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / rdsx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx.ma
index 5b62dbae165abf621a7d683fc912990e32292c76..45dd9f908f53790885b1875855e417c3df7cc253 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx.ma
@@ -12,80 +12,82 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predtysnstrong_5.ma".
+include "basic_2/notation/relations/predtysnstrong_4.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) (rdeq h o T).
+definition rdsx (h) (G) (T): predicate lenv ≝
+                             SN … (lpx h G) (rdeq T).
 
 interpretation
    "strong normalization for unbound context-sensitive parallel rt-transition on referred entries (local environment)"
-   'PRedTySNStrong h o T G L = (rdsx h o G T L).
+   'PRedTySNStrong h T G L = (rdsx h G T L).
 
 (* Basic eliminators ********************************************************)
 
 (* Basic_2A1: uses: lsx_ind *)
-lemma rdsx_ind (h) (o) (G) (T):
+lemma rdsx_ind (h) (G) (T):
                ∀Q:predicate lenv.
-               (∀L1. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
-                     (∀L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → (L1 ≛[h, o, T] L2 → ⊥) → Q L2) →
+               (∀L1. G ⊢ ⬈*[h, T] 𝐒⦃L1⦄ →
+                     (∀L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → (L1 ≛[T] L2 → ⊥) → Q L2) →
                      Q L1
                ) →
-               ∀L. G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄ →  Q L.
-#h #o #G #T #Q #H0 #L1 #H elim H -L1
+               ∀L. G ⊢ ⬈*[h, T] 𝐒⦃L⦄ →  Q L.
+#h #G #T #Q #H0 #L1 #H elim H -L1
 /5 width=1 by SN_intro/
 qed-.
 
 (* Basic properties *********************************************************)
 
 (* Basic_2A1: uses: lsx_intro *)
-lemma rdsx_intro (h) (o) (G) (T):
+lemma rdsx_intro (h) (G) (T):
                  ∀L1.
-                 (∀L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → (L1 ≛[h, o, T] L2 → ⊥) → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄) →
-                 G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄.
+                 (∀L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → (L1 ≛[T] L2 → ⊥) → G ⊢ ⬈*[h, T] 𝐒⦃L2⦄) →
+                 G ⊢ ⬈*[h, T] 𝐒⦃L1⦄.
 /5 width=1 by SN_intro/ qed.
 
 (* Basic forward lemmas *****************************************************)
 
 (* Basic_2A1: uses: lsx_fwd_pair_sn lsx_fwd_bind_sn lsx_fwd_flat_sn *)
-lemma rdsx_fwd_pair_sn (h) (o) (G):
-                       ∀I,L,V,T. G ⊢ ⬈*[h, o, ②{I}V.T] 𝐒⦃L⦄ →
-                       G ⊢ ⬈*[h, o, V] 𝐒⦃L⦄.
-#h #o #G #I #L #V #T #H
+lemma rdsx_fwd_pair_sn (h) (G):
+                       ∀I,L,V,T. G ⊢ ⬈*[h, ②{I}V.T] 𝐒⦃L⦄ →
+                       G ⊢ ⬈*[h, V] 𝐒⦃L⦄.
+#h #G #I #L #V #T #H
 @(rdsx_ind … H) -L #L1 #_ #IHL1
 @rdsx_intro #L2 #HL12 #HnL12
 /4 width=3 by rdeq_fwd_pair_sn/
 qed-.
 
 (* Basic_2A1: uses: lsx_fwd_flat_dx *)
-lemma rdsx_fwd_flat_dx (h) (o) (G):
-                       ∀I,L,V,T. G ⊢ ⬈*[h, o, ⓕ{I}V.T] 𝐒⦃L⦄ →
-                       G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄.
-#h #o #G #I #L #V #T #H 
+lemma rdsx_fwd_flat_dx (h) (G):
+                       ∀I,L,V,T. G ⊢ ⬈*[h, ⓕ{I}V.T] 𝐒⦃L⦄ →
+                       G ⊢ ⬈*[h, T] 𝐒⦃L⦄.
+#h #G #I #L #V #T #H 
 @(rdsx_ind … H) -L #L1 #_ #IHL1
 @rdsx_intro #L2 #HL12 #HnL12
 /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
+fact rdsx_fwd_pair_aux (h) (G):
+     ∀L. G ⊢ ⬈*[h, #0] 𝐒⦃L⦄ →
+     ∀I,K,V. L = K.ⓑ{I}V → G ⊢ ⬈*[h, V] 𝐒⦃K⦄.
+#h #G #L #H
 @(rdsx_ind … H) -L #L1 #_ #IH #I #K1 #V #H destruct
 /5 width=5 by lpx_pair, rdsx_intro, rdeq_fwd_zero_pair/
 qed-.
 
-lemma rdsx_fwd_pair (h) (o) (G):
-                    ∀I,K,V. G ⊢ ⬈*[h, o, #0] 𝐒⦃K.ⓑ{I}V⦄ → G ⊢ ⬈*[h, o, V] 𝐒⦃K⦄.
+lemma rdsx_fwd_pair (h) (G):
+                    ∀I,K,V. G ⊢ ⬈*[h, #0] 𝐒⦃K.ⓑ{I}V⦄ → G ⊢ ⬈*[h, V] 𝐒⦃K⦄.
 /2 width=4 by rdsx_fwd_pair_aux/ qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_2A1: uses: lsx_inv_flat *)
-lemma rdsx_inv_flat (h) (o) (G): ∀I,L,V,T. G ⊢ ⬈*[h, o, ⓕ{I}V.T] 𝐒⦃L⦄ →
-                                 ∧∧ G ⊢ ⬈*[h, o, V] 𝐒⦃L⦄ & G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄.
+lemma rdsx_inv_flat (h) (G):
+      ∀I,L,V,T. G ⊢ ⬈*[h, ⓕ{I}V.T] 𝐒⦃L⦄ →
+      ∧∧ G ⊢ ⬈*[h, V] 𝐒⦃L⦄ & G ⊢ ⬈*[h, T] 𝐒⦃L⦄.
 /3 width=3 by rdsx_fwd_pair_sn, rdsx_fwd_flat_dx, conj/ qed-.
 
 (* Basic_2A1: removed theorems 9: