new intro:

[helm.git] / helm / software / matita / nlibrary / re / re.ma

diff --git a/helm/software/matita/nlibrary/re/re.ma b/helm/software/matita/nlibrary/re/re.ma
index c33dca9bda95bbc30e53c94c9c901f7ada652869..300812ce89ccff39d7be66f2b507ad6097496684 100644 (file)
--- a/helm/software/matita/nlibrary/re/re.ma
+++ b/helm/software/matita/nlibrary/re/re.ma
@@ -65,14 +65,7 @@ nqed. *)
 
 nlemma in_l_inv_e:
  ∀S,w. in_l S w (e ?) → w = [].
- #S; #w; #H; ninversion H
-  [ #a; #b; ndestruct; //
-  | #a; #b; #c; ndestruct
-  | #a; #b; #c; #d; #e; #f; #g; #h; #i; #l; ndestruct
-  | #a; #b; #c; #d; #e; #f; #g; ndestruct
-  | #a; #b; #c; #d; #e; #f; #g; ndestruct
-  | #a; #b; #c; ndestruct
-  | #a; #b; #c; #d; #e; #f; #g; #h; #i; ndestruct ]
+ #S; #w; #H; ninversion H; #; ndestruct; //.
 nqed.
 
 naxiom in_l_inv_s: 
@@ -120,7 +113,7 @@ nlet rec eclose (S: Type[0]) (E: pre S) on E ≝
      let E1' ≝ eclose ? E1 in
      let E1'' ≝ snd … E1' in
       match fst … E1' with
-       [ true =>
+       [ true ⇒ 
           let E2' ≝ eclose ? E2 in
            〈 fst … E2', pc ? E1'' (snd … E2') 〉
        | false ⇒ 〈 false, pc ? E1'' E2 〉 ]
@@ -141,7 +134,7 @@ ntheorem eclose_true:
   true = fst bool (pre S) (eclose S E) → in_l S [] (forget S E).
  #S; #E; nelim E; nnormalize; //
   [ #H; ncases (?: False); /2/
-  | #x; #H; ncases (?: False); /2/
+  | #x H; #H; ncases (?: False); /2/
   | #x; #H; ncases (?: False); /2/
   | #w1; #w2; ncases (fst … (eclose S w1)); nnormalize; /3/;
     #_; #_; #H; ncases (?:False); /2/
@@ -165,15 +158,10 @@ nqed.
 ntheorem in_l_empty_c:
  ∀S,E1,E2. in_l S [] (c … E1 E2) → in_l S [] E2.
  #S; #E1; #E2; #H; ninversion H
-  [ #_; #H2; ndestruct
-  | #x; #K; ndestruct
+  [##1,2,4,5,6,7: #; ndestruct
   | #w1; #w2; #E1'; #E2'; #H1; #H2; #H3; #H4; #H5; #H6;
     nrewrite < H5; nlapply (eq_append_nil_to_eq_nil2 … w1 w2 ?); //;
-    ndestruct; //
-  | #w; #E1'; #E2'; #H1; #H2; #H3; #H4; ndestruct
-  | #w; #E1'; #E2'; #H1; #H2; #H3; #H4; ndestruct
-  | #E; #_; #K; ndestruct 
-  | #w1; #w2; #w3; #H1; #H2; #H3; #H4; #H5; #H6; ndestruct ]
+    ndestruct; // ]
 nqed.
 
 ntheorem eclose_true':
@@ -185,25 +173,15 @@ ntheorem eclose_true':
   | #E1; #E2; ncases (fst … (eclose S E1)); nnormalize
      [ #H1; #H2; #H3; ninversion H3; /3/;
    ##| #H1; #H2; #H3; ninversion H3
-        [ #_; #K; ndestruct
-        | #x; #K; ndestruct
+        [ ##1,2,4,5,6,7: #; ndestruct
         | #w1; #w2; #E1'; #E2'; #H4; #H5; #K1; #K2; #K3; #K4; ndestruct;
-          napply H1; nrewrite < (eq_append_nil_to_eq_nil1 … w1 w2 ?); //
-        | #w1; #E1'; #E2'; #H4; #H5; #H6; #H7; ndestruct
-        | #w1; #E1'; #E2'; #H4; #H5; #H6; #H7; ndestruct
-        | #E'; #_; #K; ndestruct
-        | #a; #b; #c; #d; #e; #f; #g; #h; #i; ndestruct ]##]
+          napply H1; nrewrite < (eq_append_nil_to_eq_nil1 … w1 w2 ?); //]##]
 ##| #E1; ncases (fst … (eclose S E1)); nnormalize; //;
     #E2; #H1; #H2; #H3; ninversion H3
-     [ #_; #K; ndestruct
-     | #w; #_; #K; ndestruct
-     | #a; #b; #c; #d; #e; #f; #g; #h; #i; #l; ndestruct
+     [ ##1,2,3,5,6,7: #; ndestruct; /2/
      | #w; #E1'; #E2'; #H1'; #H2'; #H3'; #H4; ndestruct;
        ncases (?: False); napply (absurd ?? (not_eq_true_false …));
-       /2/
-     | #w; #E1'; #E2'; #H1'; #H2'; #H3'; #H4; ndestruct; /2/
-     | #a; #b; #c; ndestruct
-     | #a; #b; #c; #d; #e; #f; #g; #h; #i; ndestruct]##]
+       /2/ ]##]
 nqed.     
 
 (*
@@ -310,6 +288,7 @@ nlet corec foo_nop (b: bool):
      | #w; nnormalize in ⊢ (??%%); napply (foo_nop false) ]##]
 nqed.
 
+(*
 nlet corec foo (a: unit):
  equiv NAT
   (eclose NAT (pc ? (ps ? 0) (pk ? (pc ? (ps ? 1) (ps ? 0)))))
@@ -329,21 +308,38 @@ nlet corec foo (a: unit):
      ##| #y; nnormalize in ⊢ (??%%); napply foo_nop
   ##]
 nqed.
+*)
 
-ndefinition test1 ≝
- pc ? (pk ? (po ? (ps ? 0) (ps ? 1))) (ps ? 0).
-
-ndefinition test2 ≝
- po ?
-  (pc ? (pk ? (pc ? (ps ? 0) (ps ? 1))) (ps ? 0))
-  (pc ? (pk ? (pc ? (ps ? 0) (ps ? 1))) (ps ? 1)).
-
-ndefinition test3 ≝
- pk ? (pc ? (pc ? (ps ? 0) (pk ? (pc ? (ps ? 0) (ps ? 1)))) (ps ? 1)).
+notation < "a \sup ⋇" non associative with precedence 90 for @{ 'pk $a}.
+notation > "a ^ *" non associative with precedence 90 for @{ 'pk $a}.
+interpretation "star" 'pk a = (pk ? a).
+                      
+notation "❨a|b❩" non associative with precedence 90 for @{ 'po $a $b}.
+interpretation "or" 'po a b = (po ? a b).
+           
+notation < "a b" non associative with precedence 60 for @{ 'pc $a $b}.
+notation > "a · b" non associative with precedence 60 for @{ 'pc $a $b}.
+interpretation "cat" 'pc a b = (pc ? a b).
+
+notation < "a" non associative with precedence 90 for @{ 'pp $a}.
+notation > "` term 90 a" non associative with precedence 90 for @{ 'pp $a}.
+interpretation "atom" 'pp a = (pp ? a).
+
+(* to get rid of \middot *)
+ncoercion rex_concat : ∀S:Type[0].∀p:pre S. pre S → pre S  ≝ pc
+on _p : pre ? to ∀_:?.?.
+(* we could also get rid of ` with a coercion from nat → pre nat *) 
+
+ndefinition test1 ≝ ❨ `0 | `1 ❩^* `0.
+ndefinition test2 ≝ ❨ (`0`1)^* `0 | (`0`1)^* `1 ❩.
+ndefinition test3 ≝ (`0 (`0`1)^* `1)^*.
 
 nlemma foo: in_moves NAT
   [0;0;1;0;1;1] (eclose ? test3) = true.
+ nnormalize in match test3;
  nnormalize;
+//;
+nqed.
 
 (**********************************************************)