notational change of lift, drop, and gget

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / lsx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx.ma
index 61363bf9f76aa3cd05b7bad297d30d86838d397e..3c2b01edd1a0f5719d95645ca9b876953f2b02bb 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx.ma
@@ -12,52 +12,98 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/lazysn_5.ma".
-include "basic_2/relocation/lleq.ma".
-include "basic_2/computation/lpxs.ma".
+include "basic_2/notation/relations/sn_6.ma".
+include "basic_2/multiple/lleq.ma".
+include "basic_2/reduction/lpx.ma".
 
 (* SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS **********************)
 
-definition lsx: ∀h. sd h → relation3 term genv lenv ≝
-                λh,g,T,G. SN … (lpxs h g G) (lleq 0 T).
+definition lsx: ∀h. sd h → relation4 ynat term genv lenv ≝
+                λh,g,d,T,G. SN … (lpx h g G) (lleq d T).
 
 interpretation
    "extended strong normalization (local environment)"
-   'LazySN h g T G L = (lsx h g T G L).
+   'SN h g d T G L = (lsx h g T d G L).
 
 (* Basic eliminators ********************************************************)
 
-lemma lsx_ind: ∀h,g,T,G. ∀R:predicate lenv.
-               (â\88\80L1. G â\8a¢ â\8b\95â¬\8a*[h, g, T] L1 →
-                     (∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → (L1 ⋕[0, T] L2 → ⊥) → R L2) →
+lemma lsx_ind: ∀h,g,G,T,d. ∀R:predicate lenv.
+               (â\88\80L1. G â\8a¢ â¬\8a*[h, g, T, d] L1 →
+                     (∀L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 → (L1 ≡[T, d] L2 → ⊥) → R L2) →
                      R L1
                ) →
-               â\88\80L. G â\8a¢ â\8b\95â¬\8a*[h, g, T] L → R L.
-#h #g #T #G #R #H0 #L1 #H elim H -L1
+               â\88\80L. G â\8a¢ â¬\8a*[h, g, T, d] L → R L.
+#h #g #G #T #d #R #H0 #L1 #H elim H -L1
 /5 width=1 by lleq_sym, SN_intro/
 qed-.
 
 (* Basic properties *********************************************************)
 
-lemma lsx_intro: ∀h,g,T,G,L1.
-                 (∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → (L1 ⋕[0, T] L2 → ⊥) → G ⊢ ⋕⬊*[h, g, T] L2) →
-                 G â\8a¢ â\8b\95â¬\8a*[h, g, T] L1.
+lemma lsx_intro: ∀h,g,G,L1,T,d.
+                 (∀L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 → (L1 ≡[T, d] L2 → ⊥) → G ⊢ ⬊*[h, g, T, d] L2) →
+                 G â\8a¢ â¬\8a*[h, g, T, d] L1.
 /5 width=1 by lleq_sym, SN_intro/ qed.
 
-lemma lsx_atom: ∀h,g,T,G. G ⊢ ⋕⬊*[h, g, T] ⋆.
-#h #g #T #G @lsx_intro
-#X #H #HT lapply (lpxs_inv_atom1 … H) -H
+lemma lsx_atom: ∀h,g,G,T,d. G ⊢ ⬊*[h, g, T, d] ⋆.
+#h #g #G #T #d @lsx_intro
+#X #H #HT lapply (lpx_inv_atom1 … H) -H
 #H destruct elim HT -HT //
 qed.
 
-lemma lsx_sort: ∀h,g,G,L,k. G ⊢ ⋕⬊*[h, g, ⋆k] L.
-#h #g #G #L1 #k @lsx_intro
+lemma lsx_sort: ∀h,g,G,L,d,k. G ⊢ ⬊*[h, g, ⋆k, d] L.
+#h #g #G #L1 #d #k @lsx_intro
 #L2 #HL12 #H elim H -H
-/3 width=4 by lpxs_fwd_length, lleq_sort/
+/3 width=4 by lpx_fwd_length, lleq_sort/
 qed.
 
-lemma lsx_gref: ∀h,g,G,L,p. G ⊢ ⋕⬊*[h, g, §p] L.
-#h #g #G #L1 #p @lsx_intro
+lemma lsx_gref: ∀h,g,G,L,d,p. G ⊢ ⬊*[h, g, §p, d] L.
+#h #g #G #L1 #d #p @lsx_intro
 #L2 #HL12 #H elim H -H
-/3 width=4 by lpxs_fwd_length, lleq_gref/
+/3 width=4 by lpx_fwd_length, lleq_gref/
 qed.
+
+lemma lsx_ge_up: ∀h,g,G,L,T,U,dt,d,e. dt ≤ yinj d + yinj e →
+                 ⬆[d, e] T ≡ U → G ⊢ ⬊*[h, g, U, dt] L → G ⊢ ⬊*[h, g, U, d] L.
+#h #g #G #L #T #U #dt #d #e #Hdtde #HTU #H @(lsx_ind … H) -L
+/5 width=7 by lsx_intro, lleq_ge_up/
+qed-.
+
+lemma lsx_ge: ∀h,g,G,L,T,d1,d2. d1 ≤ d2 →
+              G ⊢ ⬊*[h, g, T, d1] L → G ⊢ ⬊*[h, g, T, d2] L.
+#h #g #G #L #T #d1 #d2 #Hd12 #H @(lsx_ind … H) -L
+/5 width=7 by lsx_intro, lleq_ge/
+qed-.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma lsx_fwd_bind_sn: ∀h,g,a,I,G,L,V,T,d. G ⊢ ⬊*[h, g, ⓑ{a,I}V.T, d] L →
+                       G ⊢ ⬊*[h, g, V, d] L.
+#h #g #a #I #G #L #V #T #d #H @(lsx_ind … H) -L
+#L1 #_ #IHL1 @lsx_intro
+#L2 #HL12 #HV @IHL1 /3 width=4 by lleq_fwd_bind_sn/
+qed-.
+
+lemma lsx_fwd_flat_sn: ∀h,g,I,G,L,V,T,d. G ⊢ ⬊*[h, g, ⓕ{I}V.T, d] L →
+                       G ⊢ ⬊*[h, g, V, d] L.
+#h #g #I #G #L #V #T #d #H @(lsx_ind … H) -L
+#L1 #_ #IHL1 @lsx_intro
+#L2 #HL12 #HV @IHL1 /3 width=3 by lleq_fwd_flat_sn/
+qed-.
+
+lemma lsx_fwd_flat_dx: ∀h,g,I,G,L,V,T,d. G ⊢ ⬊*[h, g, ⓕ{I}V.T, d] L →
+                       G ⊢ ⬊*[h, g, T, d] L.
+#h #g #I #G #L #V #T #d #H @(lsx_ind … H) -L
+#L1 #_ #IHL1 @lsx_intro
+#L2 #HL12 #HV @IHL1 /3 width=3 by lleq_fwd_flat_dx/
+qed-.
+
+lemma lsx_fwd_pair_sn: ∀h,g,I,G,L,V,T,d. G ⊢ ⬊*[h, g, ②{I}V.T, d] L →
+                       G ⊢ ⬊*[h, g, V, d] L.
+#h #g * /2 width=4 by lsx_fwd_bind_sn, lsx_fwd_flat_sn/
+qed-.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma lsx_inv_flat: ∀h,g,I,G,L,V,T,d. G ⊢ ⬊*[h, g, ⓕ{I}V.T, d] L →
+                    G ⊢ ⬊*[h, g, V, d] L ∧ G ⊢ ⬊*[h, g, T, d] L.
+/3 width=3 by lsx_fwd_flat_sn, lsx_fwd_flat_dx, conj/ qed-.