From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Sat, 4 Oct 2014 21:05:46 +0000 (+0000)
Subject: the commit was incomplete (as is often the case :( )
X-Git-Tag: make_still_working~825
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=499eb9f9a3107c6ee4edd7b6830a1cc1b054bbe2;p=helm.git

the commit was incomplete (as is often the case :( )
---

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/fpbq_alt.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/fpbq_alt.ma
new file mode 100644
index 000000000..8bc5c210d
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/fpbq_alt.ma
@@ -0,0 +1,86 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/notation/relations/btpredalt_8.ma".
+include "basic_2/reduction/fpb_fleq.ma".
+include "basic_2/reduction/fpbq.ma".
+
+(* "QRST" PARALLEL REDUCTION FOR CLOSURES ***********************************)
+
+(* alternative definition of fpbq *)
+definition fpbqa: ∀h. sd h → tri_relation genv lenv term ≝
+                  λh,g,G1,L1,T1,G2,L2,T2.
+                  ⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ ∨ ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄.
+
+interpretation
+   "'qrst' parallel reduction (closure) alternative"
+   'BTPRedAlt h g G1 L1 T1 G2 L2 T2 = (fpbqa h g G1 L1 T1 G2 L2 T2).
+
+(* Basic properties *********************************************************)
+
+lemma fleq_fpbq: ∀h,g,G1,G2,L1,L2,T1,T2.
+                 ⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 * /2 width=1 by fpbq_lleq/
+qed.
+
+lemma fpb_fpbq: ∀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 * -G2 -L2 -T2
+/3 width=1 by fpbq_fquq, fpbq_cpx, fpbq_lpx, fqu_fquq/
+qed.
+
+(* Main properties **********************************************************)
+
+theorem fpbq_fpbqa: ∀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 * -G2 -L2 -T2
+[ #G2 #L2 #T2 #H elim (fquq_inv_gen … H) -H
+  [ /3 width=1 by fpb_fqu, or_intror/
+  | * #H1 #H2 #H3 destruct /2 width=1 by or_introl/
+  ]
+| #T2 #HT12 elim (eq_term_dec T1 T2)
+  #HnT12 destruct /4 width=1 by fpb_cpx, or_intror, or_introl/
+| #L2 #HL12 elim (lleq_dec … T1 L1 L2 0)
+  /4 width=1 by fpb_lpx, fleq_intro, or_intror, or_introl/
+| /3 width=1 by fleq_intro, or_introl/
+]
+qed.
+
+theorem fpbqa_inv_fpbq: ∀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 * /2 width=1 by fleq_fpbq, fpb_fpbq/
+qed-.
+
+(* Advanced eliminators *****************************************************)
+
+lemma fpbq_ind_alt: ∀h,g,G1,G2,L1,L2,T1,T2. ∀R:Prop.
+                    (⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ → R) →
+                    (⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R) →
+                    ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄ → R.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 #R #HI1 #HI2 #H elim (fpbq_fpbqa … H) /2 width=1 by/
+qed-.
+
+(* aternative definition of fpb *********************************************)
+
+lemma fpb_fpbq_alt: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
+                    ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄ ∧ (⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ → ⊥).
+/3 width=10 by fpb_fpbq, fpb_inv_fleq, conj/ qed.
+
+lemma fpbq_inv_fpb_alt: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h, g] ⦃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 #H0 @(fpbq_ind_alt … H) -H //
+#H elim H0 -H0 //
+qed-.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
index 0a955cb64..1aeb5138b 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
+++ b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
@@ -100,7 +100,7 @@ table {
         ]
         [ { "parallel qrst-computation" * } {
              [ "fpbg ( ⦃?,?,?⦄ >≡[?,?] ⦃?,?,?⦄ )" "fpbg_lift" + "fpbg_fleq" + "fpbg_fpbs" + "fpbg_fpbg" * ]
-             [ "fpbs ( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )" "fpbs_alt ( ⦃?,?,?⦄ ≥≥[?,?] ⦃?,?,?⦄ )" "fpbs_lift" + "fpbs_fleq" + "fpbs_aaa" + "fpbs_fpbu" + "fpbs_fpbc" + "fpbs_fpbs" * ]
+             [ "fpbs ( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )" "fpbs_alt ( ⦃?,?,?⦄ ≥≥[?,?] ⦃?,?,?⦄ )" "fpbs_lift" + "fpbs_aaa" + "fpbs_fpb" + "fpbs_fpbs" * ]
           }
         ]
         [ { "decomposed extended computation" * } {
@@ -130,9 +130,8 @@ table {
    class "water"
    [ { "reduction" * } {
         [ { "parallel qrst-reduction" * } {
-             [ "fpbc ( ⦃?,?,?⦄ ≻≡[?,?] ⦃?,?,?⦄ )" "fpbc_fleq" * ]
-             [ "fpbu ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" "fpbu_lift" + "fpbu_lleq" + "fpbu_fleq" * ]
-             [ "fpb ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )" "fpb_lift" + "fpb_aaa" * ]
+             [ "fpbq ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )" "fpbq_alt ( ⦃?,?,?⦄ ≽≽[?,?] ⦃?,?,?⦄ )" "fpbq_lift" + "fpbq_aaa" * ]
+             [ "fpb ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" "fpb_lift" + "fpb_lleq" + "fpb_fleq" * ]
           }
         ]
         [ { "normal forms for context-sensitive extended reduction" * } {