small improvements and corrections ...

diff --git a/matita/matita/contribs/lambdadelta/ground_2/lib/streams.ma b/matita/matita/contribs/lambdadelta/ground_2/lib/streams.ma
index ec7194229483c5b3642aeecc17d22bccb27b6d8b..d342a9934dc1e3c0d23b1a83b326a6d826259adf 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/lib/streams.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/lib/streams.ma
@@ -13,7 +13,6 @@
 (**************************************************************************)
 
 include "ground_2/notation/constructors/cons_2.ma".
-include "ground_2/notation/relations/exteq_3.ma".
 include "ground_2/lib/star.ma".
 
 (* STREAMS ******************************************************************)
@@ -24,59 +23,8 @@ coinductive stream (A:Type[0]): Type[0] ≝
 
 interpretation "cons (nstream)" 'Cons b t = (seq ? b t).
 
-coinductive eq_stream (A): relation (stream A) ≝
-| eq_seq: ∀t1,t2,b1,b2. b1 = b2 → eq_stream A t1 t2 → eq_stream A (b1@t1) (b2@t2)
-.
-
-interpretation "extensional equivalence (nstream)"
-   'ExtEq A t1 t2 = (eq_stream A t1 t2).
-
-definition eq_stream_repl (A) (R:relation …) ≝
-                          ∀t1,t2. t1 ≐⦋A⦌ t2 → R t1 t2.
-
-definition eq_stream_repl_back (A) (R:predicate …) ≝
-                               ∀t1. R t1 → ∀t2. t1 ≐⦋A⦌ t2 → R t2.
-
-definition eq_stream_repl_fwd (A) (R:predicate …) ≝
-                              ∀t1. R t1 → ∀t2. t2 ≐⦋A⦌ t1 → R t2.
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma eq_stream_inv_seq: ∀A,t1,t2. t1 ≐⦋A⦌ t2 →
-                         ∀u1,u2,a1,a2. a1@u1 = t1 → a2@u2 = t2 →
-                         u1 ≐ u2 ∧ a1 = a2.
-#A #t1 #t2 * -t1 -t2
-#t1 #t2 #b1 #b2 #Hb #Ht #u1 #u2 #a1 #a2 #H1 #H2 destruct /2 width=1 by conj/
-qed-.
-
 (* Basic properties *********************************************************)
 
 lemma stream_rew (A) (t:stream A): match t with [ seq a u ⇒ a @ u ] = t.
 #A * //
 qed.
-
-let corec eq_stream_refl: ∀A. reflexive … (eq_stream A) ≝ ?.
-#A * #b #t @eq_seq //
-qed.
-
-let corec eq_stream_sym: ∀A. symmetric … (eq_stream A) ≝ ?.
-#A #t1 #t2 * -t1 -t2
-#t1 #t2 #b1 #b2 #Hb #Ht @eq_seq /2 width=1 by/
-qed-.
-
-lemma eq_stream_repl_sym: ∀A,R. eq_stream_repl_back A R → eq_stream_repl_fwd A R.
-/3 width=3 by eq_stream_sym/ qed-.
-
-(* Main properties **********************************************************)
-
-let corec eq_stream_trans: ∀A. Transitive … (eq_stream A) ≝ ?.
-#A #t1 #t * -t1 -t
-#t1 #t #b1 #b * #Ht1 * #b2 #t2 #H cases (eq_stream_inv_seq A … H) -H -b
-/3 width=7 by eq_seq/
-qed-.
-
-theorem eq_stream_canc_sn: ∀A,t,t1,t2. t ≐ t1 → t ≐ t2 → t1 ≐⦋A⦌ t2.
-/3 width=3 by eq_stream_trans, eq_stream_sym/ qed-.
-
-theorem eq_stream_canc_dx: ∀A,t,t1,t2. t1 ≐ t → t2 ≐ t → t1 ≐⦋A⦌ t2.
-/3 width=3 by eq_stream_trans, eq_stream_sym/ qed-. 

diff --git a/matita/matita/contribs/lambdadelta/ground_2/lib/streams_eq.ma b/matita/matita/contribs/lambdadelta/ground_2/lib/streams_eq.ma
new file mode 100644 (file)
index 0000000..8398116
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/ground_2/lib/streams_eq.ma
@@ -0,0 +1,71 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "ground_2/notation/relations/exteq_3.ma".
+include "ground_2/lib/streams.ma".
+
+(* STREAMS ******************************************************************)
+
+coinductive eq_stream (A): relation (stream A) ≝
+| eq_seq: ∀t1,t2,b1,b2. b1 = b2 → eq_stream A t1 t2 → eq_stream A (b1@t1) (b2@t2)
+.
+
+interpretation "extensional equivalence (nstream)"
+   'ExtEq A t1 t2 = (eq_stream A t1 t2).
+
+definition eq_stream_repl (A) (R:relation …) ≝
+                          ∀t1,t2. t1 ≐⦋A⦌ t2 → R t1 t2.
+
+definition eq_stream_repl_back (A) (R:predicate …) ≝
+                               ∀t1. R t1 → ∀t2. t1 ≐⦋A⦌ t2 → R t2.
+
+definition eq_stream_repl_fwd (A) (R:predicate …) ≝
+                              ∀t1. R t1 → ∀t2. t2 ≐⦋A⦌ t1 → R t2.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma eq_stream_inv_seq: ∀A,t1,t2. t1 ≐⦋A⦌ t2 →
+                         ∀u1,u2,a1,a2. a1@u1 = t1 → a2@u2 = t2 →
+                         u1 ≐ u2 ∧ a1 = a2.
+#A #t1 #t2 * -t1 -t2
+#t1 #t2 #b1 #b2 #Hb #Ht #u1 #u2 #a1 #a2 #H1 #H2 destruct /2 width=1 by conj/
+qed-.
+
+(* Basic properties *********************************************************)
+
+let corec eq_stream_refl: ∀A. reflexive … (eq_stream A) ≝ ?.
+#A * #b #t @eq_seq //
+qed.
+
+let corec eq_stream_sym: ∀A. symmetric … (eq_stream A) ≝ ?.
+#A #t1 #t2 * -t1 -t2
+#t1 #t2 #b1 #b2 #Hb #Ht @eq_seq /2 width=1 by/
+qed-.
+
+lemma eq_stream_repl_sym: ∀A,R. eq_stream_repl_back A R → eq_stream_repl_fwd A R.
+/3 width=3 by eq_stream_sym/ qed-.
+
+(* Main properties **********************************************************)
+
+let corec eq_stream_trans: ∀A. Transitive … (eq_stream A) ≝ ?.
+#A #t1 #t * -t1 -t
+#t1 #t #b1 #b * #Ht1 * #b2 #t2 #H cases (eq_stream_inv_seq A … H) -H -b
+/3 width=7 by eq_seq/
+qed-.
+
+theorem eq_stream_canc_sn: ∀A,t,t1,t2. t ≐ t1 → t ≐ t2 → t1 ≐⦋A⦌ t2.
+/3 width=3 by eq_stream_trans, eq_stream_sym/ qed-.
+
+theorem eq_stream_canc_dx: ∀A,t,t1,t2. t1 ≐ t → t2 ≐ t → t1 ≐⦋A⦌ t2.
+/3 width=3 by eq_stream_trans, eq_stream_sym/ qed-. 

diff --git a/matita/matita/contribs/lambdadelta/ground_2/lib/streams_hdtl.ma b/matita/matita/contribs/lambdadelta/ground_2/lib/streams_hdtl.ma
index 050568754f5edc111fb8ccf948c73fc5fb34cfac..3a31efc350da7ba6e6769ce360969ddfa754b564 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/lib/streams_hdtl.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/lib/streams_hdtl.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "ground_2/notation/functions/drop_1.ma".
-include "ground_2/lib/streams.ma".
+include "ground_2/lib/streams_eq.ma".
 include "ground_2/lib/arith.ma".
 
 (* STREAMS ******************************************************************)

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sand.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sand.ma
index b830da07131debc71ccf7e60b3132e80be3e7840..85ad506a26f5582c2b84737104f65691fdeac26c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sand.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sand.ma
@@ -35,6 +35,5 @@ qed.
 let corec sand_sym: ∀f1,f2,f. f1 ⋒ f2 ≡ f → f2 ⋒ f1 ≡ f ≝ ?.
 #f1 #f2 #f * -f1 -f2 -f
 #f1 #f2 #f #g1 #g2 #g #Hf * * * -g1 -g2 -g
-[ @sand_pp | @sand_pn | @sand_np | @sand_nn ]
-[4,11,18,25: @sand_sym // |1,2,3,8,9,10,15,16,17,22,23,24: skip |*: // ]
+[ @sand_pp | @sand_pn | @sand_np | @sand_nn ] /2 width=7 by/
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/ground_2/web/ground_2_src.tbl b/matita/matita/contribs/lambdadelta/ground_2/web/ground_2_src.tbl
index 1612ee6a8aa696e1d82b802994f62a9454bd5104..cbff64690523cfb9bb2ff1a54593a09ce69d90af 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/web/ground_2_src.tbl
+++ b/matita/matita/contribs/lambdadelta/ground_2/web/ground_2_src.tbl
@@ -23,7 +23,7 @@ table {
    class "grass"
    [ { "multiple relocation" * } {
         [ { "" * } {
-             [ "rtmap" "rtmap_eq ( ? â\89\97 ? )" "rtmap_tl ( â\86\93? )" "rtmap_minus ( ? - ? )" "rtmap_isid ( 𝐈⦃?⦄ )" "rtmap_id" "rtmap_sle ( ? ⊆ ? )" "rtmap_sand ( ? ⋒ ? ≡ ? )" "rtmap_at ( @⦃?,?⦄ ≡ ? )" "rtmap_istot ( 𝐓⦃?⦄ )" "rtmap_after ( ? ⊚ ? ≡ ? )" * ]
+             [ "rtmap" "rtmap_eq ( ? â\89\97 ? )" "rtmap_tl ( ⫱? )" "rtmap_tls ( ⫱*[?]? )" "rtmap_isid ( 𝐈⦃?⦄ )" "rtmap_id" "rtmap_sle ( ? ⊆ ? )" "rtmap_sand ( ? ⋒ ? ≡ ? )" "rtmap_at ( @⦃?,?⦄ ≡ ? )" "rtmap_istot ( 𝐓⦃?⦄ )" "rtmap_after ( ? ⊚ ? ≡ ? )" * ]
              [ "nstream ( ↑? ) ( ⫯? )" "nstream_eq" "" "" "nstream_isid" "nstream_id ( 𝐈𝐝 )" "" "nstream_sand" "" "nstream_istot ( ?@❴?❵ )" "nstream_after ( ? ∘ ? )" * ]
 (*
              [ "trace ( ∥?∥ )" "trace_at ( @⦃?,?⦄ ≡ ? )" "trace_after ( ? ⊚ ? ≡ ? )" "trace_isid ( 𝐈⦃?⦄ )" "trace_isun ( 𝐔⦃?⦄ )"
@@ -37,7 +37,7 @@ table {
    class "yellow"
    [ { "extensions to the library" * } {
         [ { "" * } {
-             [ "stream ( ? @ ? ) ( ? ≐ ? )" "stream_hdtl" * ]
+             [ "stream ( ? @ ? )" "stream_eq ( ? ≐ ? )" "stream_hdtl ( ↓? )" "stream_tls ( ↓*[?]? )" * ]
              [ "list ( ◊ ) ( ? @ ? ) ( |?| )" "list2 ( ◊ ) ( {?,?} @ ? ) ( ? @@ ? ) ( |?| )" * ]
              [ "bool ( Ⓕ ) ( Ⓣ )" "arith ( ?^? ) ( ⫯? ) ( ⫰? )" * ]
              [ "star" "lstar" * ]