universary milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fleq.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fleq.ma
index 293e666d528866c8a6f83a05c3b3b3c8dc8dad93..ed03b2549a60aac5f27b7edc2cf088d7950e58a3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fleq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fleq.ma
@@ -12,67 +12,62 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/fpbc_fleq.ma".
+include "basic_2/multiple/fleq_fleq.ma".
+include "basic_2/reduction/fpbq_alt.ma".
 include "basic_2/computation/fpbg.ma".
 
-(* GENEARAL "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES *************)
+(* "QRST" PROPER PARALLEL COMPUTATION FOR CLOSURES **************************)
 
 (* Properties on lazy equivalence for closures ******************************)
 
-lemma fpbg_fleq_trans: ∀h,g,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ >≡[h, g] ⦃G, L, T⦄ →
-                       ∀G2,L2,T2. ⦃G, L, T⦄ ≡[0] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G #L1 #L #T1 #T #H @(fpbg_ind … H) -G -L -T
-[ /3 width=5 by fpbc_fpbg, fpbc_fleq_trans/
-| /4 width=9 by fpbg_strap1, fpbc_fleq_trans/
-]
+lemma fpbg_fleq_trans: ∀h,o,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ >≡[h, o] ⦃G, L, T⦄ →
+                       ∀G2,L2,T2. ⦃G, L, T⦄ ≡[0] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >≡[h, o] ⦃G2, L2, T2⦄.
+/3 width=5 by fpbg_fpbq_trans, fleq_fpbq/ qed-.
+
+lemma fleq_fpbg_trans: ∀h,o,G,G2,L,L2,T,T2. ⦃G, L, T⦄ >≡[h, o] ⦃G2, L2, T2⦄ →
+                       ∀G1,L1,T1. ⦃G1, L1, T1⦄ ≡[0] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ >≡[h, o] ⦃G2, L2, T2⦄.
+#h #o #G #G2 #L #L2 #T #T2 * #G0 #L0 #T0 #H0 #H02 #G1 #L1 #T1 #H1
+elim (fleq_fpb_trans …  H1 … H0) -G -L -T
+/4 width=9 by fpbs_strap2, fleq_fpbq, ex2_3_intro/
 qed-.
 
-lemma fleq_fpbg_trans: ∀h,g,G,G2,L,L2,T,T2. ⦃G, L, T⦄ >≡[h, g] ⦃G2, L2, T2⦄ →
-                       ∀G1,L1,T1. ⦃G1, L1, T1⦄ ≡[0] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-#h #g #G #G2 #L #L2 #T #T2 #H @(fpbg_ind_dx … H) -G -L -T
-[ /3 width=5 by fpbc_fpbg, fleq_fpbc_trans/
-| /4 width=9 by fpbg_strap2, fleq_fpbc_trans/
-]
+(* alternative definition of fpbs *******************************************)
+
+lemma fleq_fpbs: ∀h,o,G1,G2,L1,L2,T1,T2.
+                 ⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 * /2 width=1 by lleq_fpbs/
+qed.
+
+lemma fpbg_fwd_fpbs: ∀h,o,G1,G2,L1,L2,T1,T2.
+                     ⦃G1, L1, T1⦄ >≡[h,o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 *
+/3 width=5 by fpbs_strap2, fpb_fpbq/
 qed-.
 
-lemma fpbs_fpbg: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
+lemma fpbs_fpbg: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
                  ⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ ∨
-                 ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind … H) -G2 -L2 -T2
+                 ⦃G1, L1, T1⦄ >≡[h, o] ⦃G2, L2, T2⦄.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind … H) -G2 -L2 -T2
 [ /2 width=1 by or_introl/
-| #G #G2 #L #L2 #T #T2 #_ #H2 * #H1 elim (fpb_fpbu … H2) -H2 #H2
+| #G #G2 #L #L2 #T #T2 #_ #H2 * #H1 @(fpbq_ind_alt … H2) -H2 #H2
   [ /3 width=5 by fleq_trans, or_introl/
-  | /5 width=5 by fpbc_fpbg, fleq_fpbc_trans, fpbu_fpbc, or_intror/
+  | elim (fleq_fpb_trans … H1 … H2) -G -L -T
+    /4 width=5 by ex2_3_intro, or_intror, fleq_fpbs/
   | /3 width=5 by fpbg_fleq_trans, or_intror/
-  | /4 width=5 by fpbg_strap1, fpbu_fpbc, or_intror/
+  | /4 width=5 by fpbg_fpbq_trans, fpb_fpbq, or_intror/
   ]
 ]
 qed-.
 
-(* Advanced properties ******************************************************)
-
-lemma fpbg_fpb_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2.
-                      ⦃G1, L1, T1⦄ >≡[h, g] ⦃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 #H2 elim (fpb_fpbu … H2) -H2
-/3 width=5 by fpbg_fleq_trans, fpbg_strap1, fpbu_fpbc/
-qed-.
+(* Advanced properties of "qrst" parallel computation on closures ***********)
 
-
-lemma fpb_fpbg_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2.
-                      ⦃G1, L1, T1⦄ ≽[h, g] ⦃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 elim (fpb_fpbu … H1) -H1
-/3 width=5 by fleq_fpbg_trans, fpbg_strap2, fpbu_fpbc/
-qed-.
-
-lemma fpbs_fpbg_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 #H @(fpbs_ind … H) -G -L -T /3 width=5 by fpb_fpbg_trans/
-qed-.
-
-(* Note: this is used in the closure proof *)
-lemma fpbg_fpbs_trans: ∀h,g,G,G2,L,L2,T,T2. ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
-                       ∀G1,L1,T1. ⦃G1, L1, T1⦄ >≡[h, g] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-#h #g #G #G2 #L #L2 #T #T2 #H @(fpbs_ind_dx … H) -G -L -T /3 width=5 by fpbg_fpb_trans/
+lemma fpbs_fpb_trans: ∀h,o,F1,F2,K1,K2,T1,T2. ⦃F1, K1, T1⦄ ≥[h, o] ⦃F2, K2, T2⦄ →
+                      ∀G2,L2,U2. ⦃F2, K2, T2⦄ ≻[h, o] ⦃G2, L2, U2⦄ →
+                      ∃∃G1,L1,U1. ⦃F1, K1, T1⦄ ≻[h, o] ⦃G1, L1, U1⦄ & ⦃G1, L1, U1⦄ ≥[h, o] ⦃G2, L2, U2⦄.
+#h #o #F1 #F2 #K1 #K2 #T1 #T2 #H elim (fpbs_fpbg … H) -H
+[ #H12 #G2 #L2 #U2 #H2 elim (fleq_fpb_trans … H12 … H2) -F2 -K2 -T2
+  /3 width=5 by fleq_fpbs, ex2_3_intro/
+| * #H1 #H2 #H3 #H4 #H5 #H6 #H7 #H8 #H9
+  @(ex2_3_intro … H4) -H4 /3 width=5 by fpbs_strap1, fpb_fpbq/
+]
 qed-.