- "big tree" theorem is now proved up to some conjectures involving

[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 9022732dcacab28783c945872b5b2a4605ee434d..2cb1f197ed8a130105dd58046a24699cb9358e7e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fpbg.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fpbg.ma
@@ -12,39 +12,41 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/fpbs_alt.ma".
-include "basic_2/computation/fpbg.ma".
+include "basic_2/computation/fpbc_fpbs.ma".
+include "basic_2/computation/fpbg_fpns.ma".
 
 (* GENERAL "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **************)
 
-(* Advanced forward lemmas **************************************************)
+(* Advanced inversion lemmas ************************************************)
 
-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_fqup_fpbs, fpbs_trans, lpxs_fpbs, cpxs_fpbs/
+lemma fpbg_inv_fpbu_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 @(fpbg_ind_dx … H) -G1 -L1 -T1
+[ #G1 #L1 #T1 * /3 width=5 by fpns_fpbs, ex2_3_intro/
+| #G1 #G #L1 #L #T1 #T *
+  #G0 #L0 #T0 #H10 #H0 #_ *
+  /5 width=9 by fpbu_fwd_fpbs, fpbs_trans, fpns_fpbs, ex2_3_intro/
+]
 qed-.
 
-lemma fpbg_fwd_fpb_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
-[ #L2 #T2 #HT12 #H #HL12
-  elim (cpxs_neq_inv_step_sn … HT12 H) -HT12 -H
-  /4 width=9 by fpbsa_inv_fpbs, fpbc_cpx, ex3_2_intro, ex2_3_intro/
-| #G2 #L #L2 #T #T2 #HT1 #HT2 #HL2 elim (eq_term_dec T1 T) #H destruct
-  [ -HT1 elim (fqup_inv_step_sn … HT2) -HT2
-    /4 width=9 by fpbsa_inv_fpbs, fpbc_fqu, ex3_2_intro, ex2_3_intro/
-  | elim (cpxs_neq_inv_step_sn … HT1 H) -HT1 -H
-    /5 width=9 by fpbsa_inv_fpbs, fpbc_cpx, fqup_fqus, ex3_2_intro, ex2_3_intro/
-  ]
-]
+(* Advanced forward lemmas **************************************************)
+
+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 @(fpbg_ind … H) -G2 -L2 -T2
+[2: #G #G2 #L #L2 #T #T2 #_ #H2 #IH1 @(fpbs_trans … IH1) -IH1 ] (**) (* full auto fails *)
+/2 width=1 by fpbc_fwd_fpbs/
 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.
+lemma fpbs_fpbu_trans: ∀h,g,F1,F2,K1,K2,T1,T2. ⦃F1, K1, T1⦄ ≥[h, g] ⦃F2, K2, T2⦄ →
+                       ∀G2,L2,U2. ⦃F2, K2, T2⦄ ≻[h, g] ⦃G2, L2, U2⦄ →
+                       ∃∃G1,L1,U1. ⦃F1, K1, T1⦄ ≻[h, g] ⦃G1, L1, U1⦄ & ⦃G1, L1, U1⦄ ≥[h, g] ⦃G2, L2, U2⦄.
+/5 width=5 by fpbg_inv_fpbu_sn, fpbs_fpbg_trans, fpbc_fpbg, fpbu_fpbc/ qed-.
+
+(* Man properties ***********************************************************)
+
+theorem fpbg_trans: ∀h,g. tri_transitive … (fpbg h g).
+/2 width=5 by tri_TC_transitive/ qed-.
+