update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lfsx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lfsx.ma
index 5ea3071b041f5da29812ef6be0b9811b65803357..acb4447e3ea90fe82511b2258e9945569d5c3197 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lfsx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lfsx.ma
@@ -12,58 +12,67 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/static/lfdeq_lfdeq.ma".
 include "basic_2/rt_transition/lfpx_lfdeq.ma".
 include "basic_2/rt_computation/lfsx.ma".
 
 (* STRONGLY NORMALIZING LOCAL ENV.S FOR UNCOUNTED PARALLEL RT-TRANSITION ****)
 
-axiom pippo: ∀h,o,p,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈[h, V] L2 →
-             ∃∃L. ⦃G, L1⦄ ⊢ ⬈[h, ⓑ{p,I}V.T] L & L ≡[h, o, V] L2.
-
 (* Advanced properties ******************************************************)
 
+(* Basic_2A1: uses: lsx_lleq_trans *)
 lemma lfsx_lfdeq_trans: ∀h,o,G,L1,T. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
-                        â\88\80L2. L1 â\89¡[h, o, T] L2 → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄.
+                        â\88\80L2. L1 â\89\9b[h, o, T] L2 → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄.
 #h #o #G #L1 #T #H @(lfsx_ind … H) -L1
 #L1 #_ #IHL1 #L2 #HL12 @lfsx_intro
 #L #HL2 #HnL2 elim (lfdeq_lfpx_trans … HL2 … HL12) -HL2
 /4 width=5 by lfdeq_repl/
 qed-.
 
+(* Basic_2A1: uses: lsx_lpx_trans *)
+lemma lfsx_lfpx_trans: ∀h,o,G,L1,T. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
+                       ∀L2. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄.
+#h #o #G #L1 #T #H @(lfsx_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
+elim (lfdeq_dec h o L1 L2 T) /3 width=4 by lfsx_lfdeq_trans, lfxs_refl/
+qed-.
+
 (* Advanced forward lemmas **************************************************)
 
-(* Basic_2A1: was: lsx_fwd_bind_sn *)
-lemma lfsx_fwd_bind_sn: ∀h,o,p,I,G,L,V,T. G ⊢ ⬈*[h, o, ⓑ{p,I}V.T] 𝐒⦃L⦄ →
+(* Basic_2A1: uses: lsx_fwd_pair_sn lsx_fwd_bind_sn lsx_fwd_flat_sn *)
+lemma lfsx_fwd_pair_sn: ∀h,o,I,G,L,V,T. G ⊢ ⬈*[h, o, ②{I}V.T] 𝐒⦃L⦄ →
                         G ⊢ ⬈*[h, o, V] 𝐒⦃L⦄.
-#h #o #p #I #G #L #V #T #H @(lfsx_ind … H) -L
+#h #o #I #G #L #V #T #H @(lfsx_ind … H) -L
 #L1 #_ #IHL1 @lfsx_intro
-#L2 #H #HnL12 elim (pippo … o p I … T H) -H
-/6 width=4 by lfsx_lfdeq_trans, lfdeq_trans, lfdeq_fwd_bind_sn/
-qed-.
-(*
-lemma lfsx_fwd_flat_sn: ∀h,o,I,G,L,V,T,l. G ⊢ ⬈*[h, o, ⓕ{I}V.T, l] L →
-                       G ⊢ ⬈*[h, o, V, l] L.
-#h #o #I #G #L #V #T #l #H @(lfsx_ind … H) -L
-#L1 #_ #IHL1 @lfsx_intro
-#L2 #HL12 #HV @IHL1 /3 width=3 by lfdeq_fwd_flat_sn/
+#L2 #H #HnL12 elim (lfpx_pair_sn_split … H o I T) -H
+/6 width=3 by lfsx_lfdeq_trans, lfdeq_trans, lfdeq_fwd_pair_sn/
 qed-.
 
-lemma lfsx_fwd_flat_dx: ∀h,o,I,G,L,V,T,l. G ⊢ ⬈*[h, o, ⓕ{I}V.T, l] L →
-                       G ⊢ ⬈*[h, o, T, l] L.
-#h #o #I #G #L #V #T #l #H @(lfsx_ind … H) -L
+(* Basic_2A1: uses: lsx_fwd_flat_dx *)
+lemma lfsx_fwd_flat_dx: ∀h,o,I,G,L,V,T. G ⊢ ⬈*[h, o, ⓕ{I}V.T] 𝐒⦃L⦄ →
+                        G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄.
+#h #o #I #G #L #V #T #H @(lfsx_ind … H) -L
 #L1 #_ #IHL1 @lfsx_intro
-#L2 #HL12 #HV @IHL1 /3 width=3 by lfdeq_fwd_flat_dx/
+#L2 #H #HnL12 elim (lfpx_flat_dx_split … H o I V) -H
+/6 width=3 by lfsx_lfdeq_trans, lfdeq_trans, lfdeq_fwd_flat_dx/
 qed-.
 
-lemma lfsx_fwd_pair_sn: ∀h,o,I,G,L,V,T,l. G ⊢ ⬈*[h, o, ②{I}V.T, l] L →
-                       G ⊢ ⬈*[h, o, V, l] L.
-#h #o * /2 width=4 by lfsx_fwd_bind_sn, lfsx_fwd_flat_sn/
+(* Basic_2A1: uses: lsx_fwd_bind_dx *)
+(* Note: the exclusion binder (ⓧ) makes this more elegant and much simpler *)
+lemma lfsx_fwd_bind_dx: ∀h,o,p,I,G,L,V,T. G ⊢ ⬈*[h, o, ⓑ{p,I}V.T] 𝐒⦃L⦄ →
+                        G ⊢ ⬈*[h, o, T] 𝐒⦃L.ⓧ⦄.
+#h #o #p #I #G #L #V #T #H @(lfsx_ind … H) -L
+#L1 #_ #IH @lfsx_intro
+#L2 #H #HT elim (lfpx_bind_dx_split_void … H o p I V) -H
+/6 width=5 by lfsx_lfdeq_trans, lfdeq_trans, lfdeq_fwd_bind_dx_void/
 qed-.
 
-(* Basic inversion lemmas ***************************************************)
+(* Advanced inversion lemmas ************************************************)
+
+(* Basic_2A1: uses: lsx_inv_flat *)
+lemma lfsx_inv_flat: ∀h,o,I,G,L,V,T. G ⊢ ⬈*[h, o, ⓕ{I}V.T] 𝐒⦃L⦄ →
+                     G ⊢ ⬈*[h, o, V] 𝐒⦃L⦄ ∧ G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄.
+/3 width=3 by lfsx_fwd_pair_sn, lfsx_fwd_flat_dx, conj/ qed-.
 
-lemma lfsx_inv_flat: ∀h,o,I,G,L,V,T,l. G ⊢ ⬈*[h, o, ⓕ{I}V.T, l] L →
-                    G ⊢ ⬈*[h, o, V, l] L ∧ G ⊢ ⬈*[h, o, T, l] L.
-/3 width=3 by lfsx_fwd_flat_sn, lfsx_fwd_flat_dx, conj/ qed-.
-*)
\ No newline at end of file
+(* Basic_2A1: uses: lsx_inv_bind *)
+lemma lfsx_inv_bind: ∀h,o,p,I,G,L,V,T. G ⊢ ⬈*[h, o, ⓑ{p,I}V.T] 𝐒⦃L⦄ →
+                     G ⊢ ⬈*[h, o, V] 𝐒⦃L⦄ ∧ G ⊢ ⬈*[h, o, T] 𝐒⦃L.ⓧ⦄.
+/3 width=4 by lfsx_fwd_pair_sn, lfsx_fwd_bind_dx, conj/ qed-.