3rd anniversary milestone

- recursion removed from alernative definition of lpx_sn
- some corrections and updates

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_fpbs.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_fpbs.ma
index e821fe561806b2130ba234b955e3eea0361a1241..620bbe4f707247435a3da025cfdb80c50d3c3b08 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_fpbs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_fpbs.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/fpbs_alt.ma".
+include "basic_2/computation/fpbs.ma".
 
 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
 

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lpx_sn_alt.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lpx_sn_alt.ma
index 1fb1858b5ab28637ff7cda12f80262831e6a4493..4f9ae350b9348528002e04eb195abe51f7913033 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lpx_sn_alt.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lpx_sn_alt.ma
@@ -18,56 +18,17 @@ include "basic_2/relocation/lpx_sn.ma".
 (* SN POINTWISE EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS *********)
 
 (* alternative definition of lpx_sn *)
-inductive lpx_sn_alt (R:relation3 lenv term term): relation lenv ≝
-| lpx_sn_alt_intro: ∀L1,L2.
-                    (∀I1,I2,K1,K2,V1,V2,i.
-                       ⇩[i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[i] L2 ≡ K2.ⓑ{I2}V2 → I1 = I2 ∧ R K1 V1 V2
-                    ) →
-                    (∀I1,I2,K1,K2,V1,V2,i.
-                       ⇩[i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[i] L2 ≡ K2.ⓑ{I2}V2 → lpx_sn_alt R K1 K2
-                    ) → |L1| = |L2| → lpx_sn_alt R L1 L2
-.
-
-(* compact definition of lpx_sn_alt *****************************************)
-
-lemma lpx_sn_alt_ind_alt: ∀R. ∀S:relation lenv.
-                          (∀L1,L2. |L1| = |L2| → (
-                             ∀I1,I2,K1,K2,V1,V2,i.
-                             ⇩[i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[i] L2 ≡ K2.ⓑ{I2}V2 →
-                             ∧∧ I1 = I2 & R K1 V1 V2 & lpx_sn_alt R K1 K2 & S K1 K2
-                          ) → S L1 L2) →
-                          ∀L1,L2. lpx_sn_alt R L1 L2 → S L1 L2.
-#R #S #IH #L1 #L2 #H elim H -L1 -L2
-#L1 #L2 #H1 #H2 #HL12 #IH2 @IH -IH // -HL12
-#I1 #I2 #K1 #K2 #V1 #V2 #i #HLK1 #HLK2 elim (H1 … HLK1 HLK2) -H1
-/3 width=7 by and4_intro/
-qed-.
-
-lemma lpx_sn_alt_inv_alt: ∀R,L1,L2. lpx_sn_alt R L1 L2 →
-                          |L1| = |L2| ∧
-                          ∀I1,I2,K1,K2,V1,V2,i.
+definition lpx_sn_alt: relation3 lenv term term → relation lenv ≝
+                       λR,L1,L2. |L1| = |L2| ∧
+                       (∀I1,I2,K1,K2,V1,V2,i.
                           ⇩[i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[i] L2 ≡ K2.ⓑ{I2}V2 →
-                          ∧∧ I1 = I2 & R K1 V1 V2 & lpx_sn_alt R K1 K2.
-#R #L1 #L2 #H @(lpx_sn_alt_ind_alt … H) -L1 -L2
-#L1 #L2 #HL12 #IH @conj // -HL12
-#I1 #I2 #K1 #K2 #V1 #V2 #i #HLK1 #HLK2 elim (IH … HLK1 HLK2) -IH -HLK1 -HLK2
-/2 width=1 by and3_intro/
-qed-.
-
-lemma lpx_sn_alt_intro_alt: ∀R,L1,L2. |L1| = |L2| →
-                            (∀I1,I2,K1,K2,V1,V2,i.
-                               ⇩[i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[i] L2 ≡ K2.ⓑ{I2}V2 →
-                               ∧∧ I1 = I2 & R K1 V1 V2 & lpx_sn_alt R K1 K2
-                            ) → lpx_sn_alt R L1 L2.
-#R #L1 #L2 #HL12 #IH @lpx_sn_alt_intro // -HL12
-#I1 #I2 #K1 #K2 #V1 #V2 #i #HLK1 #HLK2
-elim (IH … HLK1 HLK2) -IH -HLK1 -HLK2 /2 width=1 by conj/
-qed.
+                          I1 = I2 ∧ R K1 V1 V2
+                       ).
 
 (* Basic forward lemmas ******************************************************)
 
 lemma lpx_sn_alt_fwd_length: ∀R,L1,L2. lpx_sn_alt R L1 L2 → |L1| = |L2|.
-#R #L1 #L2 #H elim (lpx_sn_alt_inv_alt … H) //
+#R #L1 #L2 #H elim H //
 qed-.
 
 (* Basic inversion lemmas ***************************************************)
@@ -79,10 +40,14 @@ qed-.
 
 lemma lpx_sn_alt_inv_pair1: ∀R,I,L2,K1,V1. lpx_sn_alt R (K1.ⓑ{I}V1) L2 →
                             ∃∃K2,V2. lpx_sn_alt R K1 K2 & R K1 V1 V2 & L2 = K2.ⓑ{I}V2.
-#R #I1 #L2 #K1 #V1 #H elim (lpx_sn_alt_inv_alt … H) -H
+#R #I1 #L2 #K1 #V1 #H elim H -H
 #H #IH elim (length_inv_pos_sn … H) -H
 #I2 #K2 #V2 #HK12 #H destruct
-elim (IH I1 I2 K1 K2 V1 V2 0) -IH /2 width=5 by ex3_2_intro/
+elim (IH I1 I2 K1 K2 V1 V2 0) //
+#H #HV12 destruct @(ex3_2_intro … K2 V2) // -HV12
+@conj // -HK12
+#J1 #J2 #L1 #L2 #W1 #W2 #i #HKL1 #HKL2 elim (IH J1 J2 L1 L2 W1 W2 (i+1)) -IH
+/2 width=1 by ldrop_drop, conj/
 qed-.
 
 lemma lpx_sn_alt_inv_atom2: ∀R,L1. lpx_sn_alt R L1 (⋆) → L1 = ⋆.
@@ -92,16 +57,20 @@ qed-.
 
 lemma lpx_sn_alt_inv_pair2: ∀R,I,L1,K2,V2. lpx_sn_alt R L1 (K2.ⓑ{I}V2) →
                             ∃∃K1,V1. lpx_sn_alt R K1 K2 & R K1 V1 V2 & L1 = K1.ⓑ{I}V1.
-#R #I2 #L1 #K2 #V2 #H elim (lpx_sn_alt_inv_alt … H) -H
+#R #I2 #L1 #K2 #V2 #H elim H -H
 #H #IH elim (length_inv_pos_dx … H) -H
 #I1 #K1 #V1 #HK12 #H destruct
-elim (IH I1 I2 K1 K2 V1 V2 0) -IH /2 width=5 by ex3_2_intro/
+elim (IH I1 I2 K1 K2 V1 V2 0) //
+#H #HV12 destruct @(ex3_2_intro … K1 V1) // -HV12
+@conj // -HK12
+#J1 #J2 #L1 #L2 #W1 #W2 #i #HKL1 #HKL2 elim (IH J1 J2 L1 L2 W1 W2 (i+1)) -IH
+/2 width=1 by ldrop_drop, conj/
 qed-.
 
 (* Basic properties *********************************************************)
 
 lemma lpx_sn_alt_atom: ∀R. lpx_sn_alt R (⋆) (⋆).
-#R @lpx_sn_alt_intro_alt //
+#R @conj //
 #I1 #I2 #K1 #K2 #V1 #V2 #i #HLK1 elim (ldrop_inv_atom1 … HLK1) -HLK1
 #H destruct
 qed.
@@ -109,14 +78,14 @@ qed.
 lemma lpx_sn_alt_pair: ∀R,I,L1,L2,V1,V2.
                        lpx_sn_alt R L1 L2 → R L1 V1 V2 →
                        lpx_sn_alt R (L1.ⓑ{I}V1) (L2.ⓑ{I}V2).
-#R #I #L1 #L2 #V1 #V2 #H #HV12 elim (lpx_sn_alt_inv_alt … H) -H
-#HL12 #IH @lpx_sn_alt_intro_alt normalize //
+#R #I #L1 #L2 #V1 #V2 #H #HV12 elim H -H
+#HL12 #IH @conj normalize //
 #I1 #I2 #K1 #K2 #W1 #W2 #i @(nat_ind_plus … i) -i
 [ #HLK1 #HLK2
   lapply (ldrop_inv_O2 … HLK1) -HLK1 #H destruct
   lapply (ldrop_inv_O2 … HLK2) -HLK2 #H destruct
-  /4 width=3 by lpx_sn_alt_intro_alt, and3_intro/
-| -HL12 -HV12 /3 width=5 by ldrop_inv_drop1/
+  /2 width=1 by conj/
+| -HL12 -HV12 /3 width=6 by ldrop_inv_drop1/
 ]
 qed.
 
@@ -142,36 +111,15 @@ qed-.
 lemma lpx_sn_intro_alt: ∀R,L1,L2. |L1| = |L2| →
                         (∀I1,I2,K1,K2,V1,V2,i.
                            ⇩[i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[i] L2 ≡ K2.ⓑ{I2}V2 →
-                           ∧∧ I1 = I2 & R K1 V1 V2 & lpx_sn R K1 K2
+                           I1 = I2 ∧ R K1 V1 V2
                         ) → lpx_sn R L1 L2.
-#R #L1 #L2 #HL12 #IH @lpx_sn_alt_inv_lpx_sn
-@lpx_sn_alt_intro_alt // -HL12
-#I1 #I2 #K1 #K2 #V1 #V2 #i #HLK1 #HLK2
-elim (IH … HLK1 HLK2) -IH -HLK1 -HLK2 /3 width=1 by lpx_sn_lpx_sn_alt, and3_intro/
-qed.
-
-lemma lpx_sn_ind_alt: ∀R. ∀S:relation lenv.
-                      (∀L1,L2. |L1| = |L2| → (
-                         ∀I1,I2,K1,K2,V1,V2,i.
-                         ⇩[i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[i] L2 ≡ K2.ⓑ{I2}V2 →
-                         ∧∧ I1 = I2 & R K1 V1 V2 & lpx_sn R K1 K2 & S K1 K2
-                      ) → S L1 L2) →
-                      ∀L1,L2. lpx_sn R L1 L2 → S L1 L2.
-#R #S #IH1 #L1 #L2 #H lapply (lpx_sn_lpx_sn_alt … H) -H
-#H @(lpx_sn_alt_ind_alt … H) -L1 -L2
-#L1 #L2 #HL12 #IH2 @IH1 -IH1 // -HL12
-#I1 #I2 #K1 #K2 #V1 #V2 #i #HLK1 #HLK2 elim (IH2 … HLK1 HLK2) -IH2 -HLK1 -HLK2
-/3 width=1 by lpx_sn_alt_inv_lpx_sn, and4_intro/
-qed-.
+/4 width=4 by lpx_sn_alt_inv_lpx_sn, conj/ qed.
 
 lemma lpx_sn_inv_alt: ∀R,L1,L2. lpx_sn R L1 L2 →
                       |L1| = |L2| ∧
                       ∀I1,I2,K1,K2,V1,V2,i.
                       ⇩[i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[i] L2 ≡ K2.ⓑ{I2}V2 →
-                      ∧∧ I1 = I2 & R K1 V1 V2 & lpx_sn R K1 K2.
+                      I1 = I2 ∧ R K1 V1 V2.
 #R #L1 #L2 #H lapply (lpx_sn_lpx_sn_alt … H) -H
-#H elim (lpx_sn_alt_inv_alt … H) -H
-#HL12 #IH @conj //
-#I1 #I2 #K1 #K2 #V1 #V2 #i #HLK1 #HLK2
-elim (IH … HLK1 HLK2) -IH -HLK1 -HLK2 /3 width=1 by lpx_sn_alt_inv_lpx_sn, and3_intro/
+#H elim H -H /3 width=4 by conj/
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2.ldw.xml b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2.ldw.xml
index cc0a402b0a2f9f084be59f80da988e4e6a1707fb..0908b1e0a017d4454141a7d79712ed6017732a67 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2.ldw.xml
+++ b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2.ldw.xml
@@ -5,6 +5,7 @@
       title = "\lambda\delta version 2"
       head = "cic:/matita/lambdadelta/basic_2/ (λδ version 2)"
 >
+<!--   
    <section>System's Syntax and Behavior</section>
    <body>This is a summary of the "block structure"
          of the System's syntactic items and reductions.
@@ -15,6 +16,7 @@
          *** In global environments only.
          **** Sort level k in terms only.
    </body>
+-->
 
    <section>Summary of the Specification</section>
    <body>Here is a numerical acount of the specification's contents
@@ -30,8 +32,13 @@
          for native type assignment.
    </news>
    <news date="In progress.">
-         Closure of context-sensitive extended computation
-         for native validity.
+         Closure of native validity
+        for context-sensitive extended computation.
+   </news>
+   <news date="2014 April 16.">
+         lazy equivalence for local environments
+        serves as irrelevant step in "big tree" computation
+         (anniversary milestone).
    </news>
    <news date="2014 January 20.">
          Parametrized slicing for local environments
@@ -61,7 +68,7 @@
          Confluence for context-free parallel reduction on closures.
    </news>
    <news date="2012 July 26.">
-         Term binders polarized to control ζ-reduction.
+         Term binders polarized to control ζ-reduction (not released).
    </news>
    <news date="2012 April 16.">
          Context-sensitive subject equivalence