- the relation for pointwise extensions now takes a binder as argument

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_alt.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_alt.ma
index cf39bffccc3b0a2608ba09717be8509507ca7612..a446b57fa26038bcb5e37026f664bdf3cfc79be8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_alt.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_alt.ma
@@ -13,17 +13,20 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/btpredstaralt_8.ma".
-include "basic_2/computation/llpxs_cpxs.ma".
-include "basic_2/computation/fpbs_fpbs.ma".
+include "basic_2/substitution/lleq_fqus.ma".
+include "basic_2/substitution/lleq_lleq.ma".
+include "basic_2/computation/cpxs_lleq.ma".
+include "basic_2/computation/lpxs_lleq.ma".
+include "basic_2/computation/fpbs.ma".
 
 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
 
 (* Note: alternative definition of fpbs *)
 definition fpbsa: ∀h. sd h → tri_relation genv lenv term ≝
                   λh,g,G1,L1,T1,G2,L2,T2.
-                  ∃∃L,T. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T &
-                         â¦\83G1, L1, Tâ¦\84 â\8a\83* â¦\83G2, L, T2⦄ &
-                         ⦃G2, L⦄ ⊢ ➡*[h, g, T2, 0] L2.
+                  ∃∃L0,L,T. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T &
+                         â¦\83G1, L1, Tâ¦\84 â\8a\90* â¦\83G2, L0, T2⦄ &
+                         ⦃G2, L0⦄ ⊢ ➡*[h, g] L & L ⋕[T2, 0] L2.
 
 interpretation "'big tree' parallel computation (closure) alternative"
    'BTPRedStarAlt h g G1 L1 T1 G2 L2 T2 = (fpbsa h g G1 L1 T1 G2 L2 T2).
@@ -32,15 +35,19 @@ interpretation "'big tree' parallel computation (closure) alternative"
 
 lemma fpb_fpbsa_trans: ∀h,g,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G, L, T⦄ →
                        ∀G2,L2,T2. ⦃G, L, T⦄ ≥≥[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥≥[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G #L1 #L #T1 #T * -G -L -T [ #G #L #T #HG1 | #T #HT1 | #L #HL1 ]
-#G2 #L2 #T2 * #L0 #T0 #HT0 #HG2 #HL02
+#h #g #G1 #G #L1 #L #T1 #T * -G -L -T [ #G #L #T #HG1 | #T #HT1 | #L #HL1 | #L #HL1 ]
+#G2 #L2 #T2 * #L00 #L0 #T0 #HT0 #HG2 #HL00 #HL02
 [ elim (fquq_cpxs_trans … HT0 … HG1) -T
-  /3 width=7 by fqus_strap2, ex3_2_intro/
-| /3 width=5 by cpxs_strap2, ex3_2_intro/
-| lapply (llpx_cpxs_trans … HT0 … HL1) -HT0 #HT10
-  lapply (cpxs_llpx_conf … HT10 … HL1) -HL1 #HL1
-  elim (llpx_fqus_trans … HG2 … HL1) -L
-  /3 width=7 by llpxs_strap2, cpxs_trans, ex3_2_intro/
+  /3 width=7 by fqus_strap2, ex4_3_intro/
+| /3 width=7 by cpxs_strap2, ex4_3_intro/
+| lapply (lpx_cpxs_trans … HT0 … HL1) -HT0 #HT10
+  elim (lpx_fqus_trans … HG2 … HL1) -L
+  /3 width=7 by lpxs_strap2, cpxs_trans, ex4_3_intro/
+| lapply (lleq_cpxs_trans … HT0 … HL1) -HT0 #HT0
+  lapply (cpxs_lleq_conf_sn … HT0 … HL1) -HL1 #HL1
+  elim (lleq_fqus_trans … HG2 … HL1) -L #K00 #HG12 #HKL00
+  elim (lleq_lpxs_trans … HL00 … HKL00) -L00
+  /3 width=9 by lleq_trans, ex4_3_intro/
 ]
 qed-.
 
@@ -49,7 +56,7 @@ qed-.
 theorem fpbs_fpbsa: ∀h,g,G1,G2,L1,L2,T1,T2.
                     ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥≥[h, g] ⦃G2, L2, T2⦄.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind_dx … H) -G1 -L1 -T1
-/2 width=5 by fpb_fpbsa_trans, ex3_2_intro/
+/2 width=7 by fpb_fpbsa_trans, ex4_3_intro/
 qed.
 
 (* Main inversion lemmas ****************************************************)
@@ -57,5 +64,20 @@ qed.
 theorem fpbsa_inv_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2.
                         ⦃G1, L1, T1⦄ ≥≥[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 *
-/4 width=5 by fpbs_trans, fqus_fpbs, cpxs_fpbs, llpxs_fpbs/
+/3 width=5 by cpxs_fqus_lpxs_fpbs, fpbs_strap1, fpb_lleq/
 qed-.
+
+(* Advanced properties ******************************************************)
+
+lemma fpbs_intro_alt: ∀h,g,G1,G2,L1,L0,L,L2,T1,T,T2.
+                      ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T → ⦃G1, L1, T⦄ ⊐* ⦃G2, L0, T2⦄ →
+                      ⦃G2, L0⦄ ⊢ ➡*[h, g] L → L ⋕[T2, 0] L2 →  ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ .
+/3 width=7 by fpbsa_inv_fpbs, ex4_3_intro/ qed.
+
+(* Advanced inversion lemmas *************************************************)
+
+lemma fpbs_inv_alt: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
+                    ∃∃L0,L,T. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T &
+                              ⦃G1, L1, T⦄ ⊐* ⦃G2, L0, T2⦄ &
+                              ⦃G2, L0⦄ ⊢ ➡*[h, g] L & L ⋕[T2, 0] L2.
+/2 width=1 by  fpbs_fpbsa/ qed-.