universary milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fpbg.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fpbg.ma
index 97846fda46c420ff2a0d961694b9be3d048b0c9c..28748f278a28697ba64db54d596149940c6188cf 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fpbg.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fpbg.ma
@@ -12,46 +12,11 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/lpxs_lpxs.ma".
-include "basic_2/computation/fpbs_alt.ma".
-include "basic_2/computation/fpbg.ma".
+include "basic_2/computation/fpbg_fpbs.ma".
 
-(* GENERAL "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **************)
+(* "QRST" PROPER PARALLEL COMPUTATION FOR CLOSURES **************************)
 
-(* Advanced forward lemmas **************************************************)
+(* Main properties **********************************************************)
 
-lemma fpbg_fwd_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 #H elim H -G2 -L2 -T2
-/3 width=5 by cpxs_fqus_lpxs_fpbs, cpxs_fqup_fpbs, fpbs_trans, lpxs_fpbs, cpxs_fpbs/
-qed-.
-
-lemma fpbg_fwd_fpbc_sn: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄ →
-                        ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G2 -L2 -T2
-[ /4 width=5 by fpbc_cpxs, lpxs_fpbs, ex2_3_intro/
-| #G2 #L #L2 #T #T2 #HT1 #HT2 #HL2 elim (eq_term_dec T1 T) #H destruct
-  [ -HT1 /3 width=5 by fpbc_fqup, lpxs_fpbs, ex2_3_intro/
-  | /5 width=9 by fpbc_cpxs, fpbsa_inv_fpbs, fqup_fqus, ex3_2_intro, ex2_3_intro/
-  ]
-| #G2 #L #L0 #L2 #T #T2 #HT1 #HT2 #HL0 #H0 #HL02 #H02
-  lapply (lpxs_trans … HL0 … HL02) #HL2
-  elim (eq_term_dec T1 T) #H destruct
-  [ -HT1 elim (fqus_inv_gen … HT2) -HT2
-    [ /3 width=5 by fpbc_fqup, lpxs_fpbs, ex2_3_intro/
-    | * #H1 #H2 #H3 destruct
-      /4 width=5 by fpbc_lpxs, lpxs_fpbs, ex2_3_intro/
-    ]
-  | /4 width=9 by fpbc_cpxs, fpbsa_inv_fpbs, ex3_2_intro, ex2_3_intro/
-  ]
-]
-qed-.
-
-(* Advanced properties ******************************************************)
-
-lemma fqu_fpbs_fpbg: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G, L, T⦄ →
-                     ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H elim(fpbs_fpbsa … H) -H
-#L0 #T0 #HT0 #HT02 #HL02 elim (fqu_cpxs_trans … HT0 … H1) -T
-/3 width=7 by fpbg_fqup, fqus_strap2_fqu/
-qed.
+theorem fpbg_trans: ∀h,o. tri_transitive … (fpbg h o).
+/3 width=5 by fpbg_fpbs_trans, fpbg_fwd_fpbs/ qed-.