first and second commutation property on lazy equivalence for

[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 f04f3587fc803bce96cd970d707802395b0a1c11..36fc552641502eb55d35a1ffea2d0bcbe8659321 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_alt.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_alt.ma
@@ -13,6 +13,7 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/btpredstaralt_8.ma".
+include "basic_2/computation/lpxs_cpxs.ma".
 include "basic_2/computation/fpbs_fpbs.ma".
 
 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
@@ -20,15 +21,40 @@ include "basic_2/computation/fpbs_fpbs.ma".
 (* 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⦄ ⊃* ⦃G2, L, T⦄ & ⦃G2, L⦄ ⊢ T ➡*[h, g] T2 & ⦃G2, L⦄ ⊢ ➡*[h, g] L2.
+                  ∃∃L,T. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T &
+                         ⦃G1, L1, T⦄ ⊃* ⦃G2, L, T2⦄ &
+                         ⦃G2, L⦄ ⊢ ➡*[h, g] 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).
 
+(* Basic properties *********************************************************)
+
+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
+[ 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 (lpx_cpxs_trans … HT0 … HL1) -HT0
+  elim (lpx_fqus_trans … HG2 … HL1) -L
+  /3 width=7 by lpxs_strap2, cpxs_trans, ex3_2_intro/
+] 
+qed-.
+
+(* Main properties **********************************************************)
+
+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/
+qed.
+
 (* Main inversion lemmas ****************************************************)
 
 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, fsups_fpbs, cpxs_fpbs, lpxs_fpbs/
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 *
+/4 width=5 by fpbs_trans, fqus_fpbs, cpxs_fpbs, lpxs_fpbs/
 qed-.