X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=weblib%2Ftutorial%2Fchapter7.ma;h=e37ec25e6d3689c0be83211ace41b47a3bb320e8;hb=a82d87a4c2ff9f518385fba7357dafb632a22882;hp=a4e3a861472a54c5c207646ecb2c0ffcd5067fa5;hpb=fc43587e06d59afb5b1c65904372843d928fdfe5;p=helm.git

diff --git a/weblib/tutorial/chapter7.ma b/weblib/tutorial/chapter7.ma
index a4e3a8614..e37ec25e6 100644
--- a/weblib/tutorial/chapter7.ma
+++ b/weblib/tutorial/chapter7.ma
@@ -8,7 +8,7 @@ include "tutorial/chapter6.ma".
 (* The type re of regular expressions over an alphabet $S$ is the smallest 
 collection of objects generated by the following constructors: *)
 
-inductive re (S: a href="cic:/matita/tutorial/chapter4/DeqSet.ind(1,0,0)"DeqSet/a) : Type[0] ≝
+img class="anchor" src="icons/tick.png" id="re"inductive re (S: a href="cic:/matita/tutorial/chapter4/DeqSet.ind(1,0,0)"DeqSet/a) : Type[0] ≝
    z: re S                (* empty: ∅ *)
  | e: re S                (* epsilon: ϵ *)
  | s: S → re S            (* symbol: a *)
@@ -31,20 +31,20 @@ interpretation "empty" 'empty = (z ?).
 (* The language sem{e} associated with the regular expression e is inductively 
 defined by the following function: *)
 
-let rec in_l (S : a href="cic:/matita/tutorial/chapter4/DeqSet.ind(1,0,0)"DeqSet/a) (r : a href="cic:/matita/tutorial/chapter7/re.ind(1,0,1)"re/a S) on r : a href="cic:/matita/tutorial/chapter6/word.def(3)"word/a S → Prop ≝ 
+img class="anchor" src="icons/tick.png" id="in_l"let rec in_l (S : a href="cic:/matita/tutorial/chapter4/DeqSet.ind(1,0,0)"DeqSet/aspan class="error" title="Parse error: RPAREN expected after [term] (in [arg])"/span) (r : a href="cic:/matita/tutorial/chapter7/re.ind(1,0,1)"re/a S) on r : a href="cic:/matita/tutorial/chapter6/word.def(3)"word/aspan class="error" title="Parse error: SYMBOL '≝' expected (in [let_defs])"/span S → Prop ≝ 
 match r with
 [ z ⇒ a title="empty set" href="cic:/fakeuri.def(1)"∅/a
-| e ⇒ a title="singleton" href="cic:/fakeuri.def(1)"{/aa title="epsilon" href="cic:/fakeuri.def(1)"ϵ/a}
-| s x ⇒ a title="singleton" href="cic:/fakeuri.def(1)"{/a (xa title="cons" href="cic:/fakeuri.def(1)":/a:a title="nil" href="cic:/fakeuri.def(1)"[/a]) }
+| e ⇒ a title="singleton" href="cic:/fakeuri.def(1)"{/aa title="epsilon" href="cic:/fakeuri.def(1)"ϵ/aa title="singleton" href="cic:/fakeuri.def(1)"}/a
+| s x ⇒ a title="singleton" href="cic:/fakeuri.def(1)"{/aspan class="error" title="Parse error: [ident] or [term level 19] expected after [sym{] (in [term])"/span (xa title="cons" href="cic:/fakeuri.def(1)":/aa title="cons" href="cic:/fakeuri.def(1)":/aa title="nil" href="cic:/fakeuri.def(1)"[/aa title="nil" href="cic:/fakeuri.def(1)"]/a) a title="singleton" href="cic:/fakeuri.def(1)"}/a
 | c r1 r2 ⇒ (in_l ? r1) a title="cat lang" href="cic:/fakeuri.def(1)"·/a (in_l ? r2)
 | o r1 r2 ⇒ (in_l ? r1) a title="union" href="cic:/fakeuri.def(1)"∪/a (in_l ? r2)
-| k r1 ⇒ (in_l ? r1) a title="star lang" href="cic:/fakeuri.def(1)"^/a*].
+| k r1 ⇒ (in_l ? r1) a title="star lang" href="cic:/fakeuri.def(1)"^/aa title="star lang" href="cic:/fakeuri.def(1)"*/a].
 
 notation "\sem{term 19 E}" non associative with precedence 75 for @{'in_l $E}.
 interpretation "in_l" 'in_l E = (in_l ? E).
 interpretation "in_l mem" 'mem w l = (in_l ? l w).
 
-lemma rsem_star : ∀S.∀r: a href="cic:/matita/tutorial/chapter7/re.ind(1,0,1)"re/a S. a title="in_l" href="cic:/fakeuri.def(1)"\sem/a{ra title="re star" href="cic:/fakeuri.def(1)"^/a*} a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="in_l" href="cic:/fakeuri.def(1)"\sem/a{r}a title="star lang" href="cic:/fakeuri.def(1)"^/a*.
+img class="anchor" src="icons/tick.png" id="rsem_star"lemma rsem_star : ∀S.∀r: a href="cic:/matita/tutorial/chapter7/re.ind(1,0,1)"re/a S. a title="in_l" href="cic:/fakeuri.def(1)"\sem/a{ra title="re star" href="cic:/fakeuri.def(1)"^/aa title="re star" href="cic:/fakeuri.def(1)"*/aa title="in_l" href="cic:/fakeuri.def(1)"}/a a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="in_l" href="cic:/fakeuri.def(1)"\sem/a{ra title="in_l" href="cic:/fakeuri.def(1)"}/aa title="star lang" href="cic:/fakeuri.def(1)"^/aa title="star lang" href="cic:/fakeuri.def(1)"*/a.
 // qed.
 
 
@@ -78,7 +78,7 @@ formalization of the metatheory of programming languages. For our purposes, it i
 enough to mark positions preceding individual characters, so we shall have two kinds 
 of characters •a (pp a) and a (ps a) according to the case a is pointed or not. *)
 
-inductive pitem (S: a href="cic:/matita/tutorial/chapter4/DeqSet.ind(1,0,0)"DeqSet/a) : Type[0] ≝
+img class="anchor" src="icons/tick.png" id="pitem"inductive pitem (S: a href="cic:/matita/tutorial/chapter4/DeqSet.ind(1,0,0)"DeqSet/a) : Type[0] ≝
    pz: pitem S                       (* empty *)
  | pe: pitem S                       (* epsilon *)
  | ps: S → pitem S                   (* symbol *)
@@ -93,7 +93,7 @@ the end of the expression. As we shall see, pointed regular expressions can be
 understood as states of a DFA, and the boolean indicates if
 the state is final or not. *)
 
-definition pre ≝ λS.a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S a title="Product" href="cic:/fakeuri.def(1)"×/a a href="cic:/matita/basics/bool/bool.ind(1,0,0)"bool/a.
+img class="anchor" src="icons/tick.png" id="pre"definition pre ≝ λS.a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S a title="Product" href="cic:/fakeuri.def(1)"×/a a href="cic:/matita/basics/bool/bool.ind(1,0,0)"bool/a.
 
 interpretation "pitem star" 'star a = (pk ? a).
 interpretation "pitem or" 'plus a b = (po ? a b).
@@ -109,27 +109,27 @@ interpretation "pitem empty" 'empty = (pz ?).
 removing all the points. Similarly, the carrier of a pointed regular expression 
 is the carrier of its item. *)
 
-let rec forget (S: a href="cic:/matita/tutorial/chapter4/DeqSet.ind(1,0,0)"DeqSet/a) (l : a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S) on l: a href="cic:/matita/tutorial/chapter7/re.ind(1,0,1)"re/a S ≝
+img class="anchor" src="icons/tick.png" id="forget"let rec forget (S: a href="cic:/matita/tutorial/chapter4/DeqSet.ind(1,0,0)"DeqSet/a) (l : a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S) on l: a href="cic:/matita/tutorial/chapter7/re.ind(1,0,1)"re/a S ≝
  match l with
   [ pz ⇒ a href="cic:/matita/tutorial/chapter7/re.con(0,1,1)"z/a ? (* `∅ *)
   | pe ⇒ a title="re epsilon" href="cic:/fakeuri.def(1)"ϵ/a
   | ps x ⇒ a title="atom" href="cic:/fakeuri.def(1)"`/ax
   | pp x ⇒ a title="atom" href="cic:/fakeuri.def(1)"`/ax
   | pc E1 E2 ⇒ (forget ? E1) a title="re cat" href="cic:/fakeuri.def(1)"·/a (forget ? E2)
-  | po E1 E2 ⇒ (forget ? E1) a title="re or" href="cic:/fakeuri.def(1)"+/a (forget ? E2)
-  | pk E ⇒ (forget ? E)a title="re star" href="cic:/fakeuri.def(1)"^/a* ].
+  | po E1 E2 ⇒ (forget ? E1) a title="re or" href="cic:/fakeuri.def(1)"+/aspan class="error" title="Parse error: [term] expected after [sym+] (in [term])"/span (forget ? E2)
+  | pk E ⇒ (forget ? E)a title="re star" href="cic:/fakeuri.def(1)"^/aa title="re star" href="cic:/fakeuri.def(1)"*/a ].
  
 (* notation < "|term 19 e|" non associative with precedence 70 for @{'forget $e}.*)
 interpretation "forget" 'norm a = (forget ? a).
 
-lemma erase_dot : ∀S.∀e1,e2:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S. a title="forget" href="cic:/fakeuri.def(1)"|/ae1 a title="pitem cat" href="cic:/fakeuri.def(1)"·/a e2| a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a href="cic:/matita/tutorial/chapter7/re.con(0,4,1)"c/a ? (a title="forget" href="cic:/fakeuri.def(1)"|/ae1|) (a title="forget" href="cic:/fakeuri.def(1)"|/ae2|).
+img class="anchor" src="icons/tick.png" id="erase_dot"lemma erase_dot : ∀S.∀e1,e2:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S. a title="forget" href="cic:/fakeuri.def(1)"|/ae1 a title="pitem cat" href="cic:/fakeuri.def(1)"·/a e2a title="forget" href="cic:/fakeuri.def(1)"|/a a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a href="cic:/matita/tutorial/chapter7/re.con(0,4,1)"c/a ? (a title="forget" href="cic:/fakeuri.def(1)"|/ae1a title="forget" href="cic:/fakeuri.def(1)"|/a) (a title="forget" href="cic:/fakeuri.def(1)"|/ae2a title="forget" href="cic:/fakeuri.def(1)"|/a).
 // qed.
 
-lemma erase_plus : ∀S.∀i1,i2:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S.
-  a title="forget" href="cic:/fakeuri.def(1)"|/ai1 a title="pitem or" href="cic:/fakeuri.def(1)"+/a i2| a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="forget" href="cic:/fakeuri.def(1)"|/ai1| a title="re or" href="cic:/fakeuri.def(1)"+/a a title="forget" href="cic:/fakeuri.def(1)"|/ai2|.
+img class="anchor" src="icons/tick.png" id="erase_plus"lemma erase_plus : ∀S.∀i1,i2:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S.
+  a title="forget" href="cic:/fakeuri.def(1)"|/ai1 a title="pitem or" href="cic:/fakeuri.def(1)"+/a i2a title="forget" href="cic:/fakeuri.def(1)"|/a a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="forget" href="cic:/fakeuri.def(1)"|/ai1a title="forget" href="cic:/fakeuri.def(1)"|/a a title="re or" href="cic:/fakeuri.def(1)"+/a a title="forget" href="cic:/fakeuri.def(1)"|/ai2a title="forget" href="cic:/fakeuri.def(1)"|/a.
 // qed.
 
-lemma erase_star : ∀S.∀i:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S.a title="forget" href="cic:/fakeuri.def(1)"|/aia title="pitem star" href="cic:/fakeuri.def(1)"^/a*| a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="forget" href="cic:/fakeuri.def(1)"|/ai|a title="re star" href="cic:/fakeuri.def(1)"^/a*. 
+img class="anchor" src="icons/tick.png" id="erase_star"lemma erase_star : ∀S.∀i:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S.a title="forget" href="cic:/fakeuri.def(1)"|/aia title="pitem star" href="cic:/fakeuri.def(1)"^/aa title="pitem star" href="cic:/fakeuri.def(1)"*/aa title="forget" href="cic:/fakeuri.def(1)"|/a a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="forget" href="cic:/fakeuri.def(1)"|/aia title="forget" href="cic:/fakeuri.def(1)"|/aa title="re star" href="cic:/fakeuri.def(1)"^/aa title="re star" href="cic:/fakeuri.def(1)"*/a. 
 // qed.
 
 (* 
@@ -139,22 +139,22 @@ and enumerated. In particular, we can define a boolean equality beqitem and a pr
 beqitem_true that it refects propositional equality, enriching the set (pitem S)
 to a DeqSet. *)
 
-let rec beqitem S (i1,i2: a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S) on i1 ≝ 
+img class="anchor" src="icons/tick.png" id="beqitem"let rec beqitem S (i1,i2: a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S) on i1 ≝ 
   match i1 with
   [ pz ⇒ match i2 with [ pz ⇒ a href="cic:/matita/basics/bool/bool.con(0,1,0)"true/a | _ ⇒ a href="cic:/matita/basics/bool/bool.con(0,2,0)"false/a]
   | pe ⇒ match i2 with [ pe ⇒ a href="cic:/matita/basics/bool/bool.con(0,1,0)"true/a | _ ⇒ a href="cic:/matita/basics/bool/bool.con(0,2,0)"false/a]
-  | ps y1 ⇒ match i2 with [ ps y2 ⇒ y1a title="eqb" href="cic:/fakeuri.def(1)"=/a=y2 | _ ⇒ a href="cic:/matita/basics/bool/bool.con(0,2,0)"false/a]
-  | pp y1 ⇒ match i2 with [ pp y2 ⇒ y1a title="eqb" href="cic:/fakeuri.def(1)"=/a=y2 | _ ⇒ a href="cic:/matita/basics/bool/bool.con(0,2,0)"false/a]
+  | ps y1 ⇒ match i2 with [ ps y2 ⇒ y1a title="eqb" href="cic:/fakeuri.def(1)"=/aa title="eqb" href="cic:/fakeuri.def(1)"=/ay2 | _ ⇒ a href="cic:/matita/basics/bool/bool.con(0,2,0)"false/a]
+  | pp y1 ⇒ match i2 with [ pp y2 ⇒ y1a title="eqb" href="cic:/fakeuri.def(1)"=/aa title="eqb" href="cic:/fakeuri.def(1)"=/ay2 | _ ⇒ a href="cic:/matita/basics/bool/bool.con(0,2,0)"false/a]
   | po i11 i12 ⇒ match i2 with 
     [ po i21 i22 ⇒ beqitem S i11 i21 a title="boolean and" href="cic:/fakeuri.def(1)"∧/a beqitem S i12 i22
-    | _ ⇒ a href="cic:/matita/basics/bool/bool.con(0,2,0)"false/a]
+    | _ ⇒ a href="cic:/matita/basics/bool/bool.con(0,2,0)"false/aspan class="error" title="Parse error: SYMBOL '|' or SYMBOL ']' expected (in [term])"/span]
   | pc i11 i12 ⇒ match i2 with 
     [ pc i21 i22 ⇒ beqitem S i11 i21 a title="boolean and" href="cic:/fakeuri.def(1)"∧/a beqitem S i12 i22
     | _ ⇒ a href="cic:/matita/basics/bool/bool.con(0,2,0)"false/a]
   | pk i11 ⇒ match i2 with [ pk i21 ⇒ beqitem S i11 i21 | _ ⇒ a href="cic:/matita/basics/bool/bool.con(0,2,0)"false/a]
   ].
 
-lemma beqitem_true: ∀S,i1,i2. a href="cic:/matita/basics/logic/iff.def(1)"iff/a (a href="cic:/matita/tutorial/chapter7/beqitem.fix(0,1,4)"beqitem/a S i1 i2 a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a href="cic:/matita/basics/bool/bool.con(0,1,0)"true/a) (i1 a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a i2). 
+img class="anchor" src="icons/tick.png" id="beqitem_true"lemma beqitem_true: ∀S,i1,i2. a href="cic:/matita/basics/logic/iff.def(1)"iff/a (a href="cic:/matita/tutorial/chapter7/beqitem.fix(0,1,4)"beqitem/a S i1 i2 a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a href="cic:/matita/basics/bool/bool.con(0,1,0)"true/a) (i1 a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a i2). 
 #S #i1 elim i1
   [#i2 cases i2 [||#a|#a|#i21 #i22| #i21 #i22|#i3] % // normalize #H destruct
   |#i2 cases i2 [||#a|#a|#i21 #i22| #i21 #i22|#i3] % // normalize #H destruct
@@ -184,7 +184,7 @@ lemma beqitem_true: ∀S,i1,i2. a href="cic:/matita/basics/logic/iff.def(1)"if
   ]
 qed. 
 
-definition DeqItem ≝ λS.
+img class="anchor" src="icons/tick.png" id="DeqItem"definition DeqItem ≝ λS.
   a href="cic:/matita/tutorial/chapter4/DeqSet.con(0,1,0)"mk_DeqSet/a (a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S) (a href="cic:/matita/tutorial/chapter7/beqitem.fix(0,1,4)"beqitem/a S) (a href="cic:/matita/tutorial/chapter7/beqitem_true.def(5)"beqitem_true/a S).
 
 (* We also add a couple of unification hints to allow the type inference system 
@@ -207,57 +207,57 @@ The intuitive semantic of a point is to mark the position where
 we should start reading the regular expression. The language associated
 to a pre is the union of the languages associated with its points. *)
 
-let rec in_pl (S : a href="cic:/matita/tutorial/chapter4/DeqSet.ind(1,0,0)"DeqSet/a) (r : a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S) on r : a href="cic:/matita/tutorial/chapter6/word.def(3)"word/a S → Prop ≝ 
+img class="anchor" src="icons/tick.png" id="in_pl"let rec in_pl (S : a href="cic:/matita/tutorial/chapter4/DeqSet.ind(1,0,0)"DeqSet/a) (r : a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S) on r : a href="cic:/matita/tutorial/chapter6/word.def(3)"word/a S → Prop ≝ 
 match r with
 [ pz ⇒ a title="empty set" href="cic:/fakeuri.def(1)"∅/a
 | pe ⇒ a title="empty set" href="cic:/fakeuri.def(1)"∅/a
 | ps _ ⇒ a title="empty set" href="cic:/fakeuri.def(1)"∅/a
-| pp x ⇒ a title="singleton" href="cic:/fakeuri.def(1)"{/a (xa title="cons" href="cic:/fakeuri.def(1)":/a:a title="nil" href="cic:/fakeuri.def(1)"[/a]) }
-| pc r1 r2 ⇒ (in_pl ? r1) a title="cat lang" href="cic:/fakeuri.def(1)"·/a a title="in_l" href="cic:/fakeuri.def(1)"\sem/a{a href="cic:/matita/tutorial/chapter7/forget.fix(0,1,3)"forget/a ? r2} a title="union" href="cic:/fakeuri.def(1)"∪/a (in_pl ? r2)
+| pp x ⇒ a title="singleton" href="cic:/fakeuri.def(1)"{/a (xa title="cons" href="cic:/fakeuri.def(1)":/aa title="cons" href="cic:/fakeuri.def(1)":/aa title="nil" href="cic:/fakeuri.def(1)"[/aa title="nil" href="cic:/fakeuri.def(1)"]/a) a title="singleton" href="cic:/fakeuri.def(1)"}/a
+| pc r1 r2 ⇒ (in_pl ? r1) a title="cat lang" href="cic:/fakeuri.def(1)"·/a a title="in_l" href="cic:/fakeuri.def(1)"\sem/a{a href="cic:/matita/tutorial/chapter7/forget.fix(0,1,3)"forget/a ? r2a title="in_l" href="cic:/fakeuri.def(1)"}/a a title="union" href="cic:/fakeuri.def(1)"∪/aspan class="error" title="Parse error: [term] expected after [sym∪] (in [term])"/span (in_pl ? r2)
 | po r1 r2 ⇒ (in_pl ? r1) a title="union" href="cic:/fakeuri.def(1)"∪/a (in_pl ? r2)
-| pk r1 ⇒ (in_pl ? r1) a title="cat lang" href="cic:/fakeuri.def(1)"·/a a title="in_l" href="cic:/fakeuri.def(1)"\sem/a{a href="cic:/matita/tutorial/chapter7/forget.fix(0,1,3)"forget/a ? r1}a title="star lang" href="cic:/fakeuri.def(1)"^/a*  ].
+| pk r1 ⇒ (in_pl ? r1) a title="cat lang" href="cic:/fakeuri.def(1)"·/a a title="in_l" href="cic:/fakeuri.def(1)"\sem/a{a href="cic:/matita/tutorial/chapter7/forget.fix(0,1,3)"forget/a ? r1a title="in_l" href="cic:/fakeuri.def(1)"}/aa title="star lang" href="cic:/fakeuri.def(1)"^/aa title="star lang" href="cic:/fakeuri.def(1)"*/a  ].
 
 interpretation "in_pl" 'in_l E = (in_pl ? E).
 interpretation "in_pl mem" 'mem w l = (in_pl ? l w).
 
-definition in_prl ≝ λS : a href="cic:/matita/tutorial/chapter4/DeqSet.ind(1,0,0)"DeqSet/a.λp:a href="cic:/matita/tutorial/chapter7/pre.def(1)"pre/a S. 
-  if (a title="pair pi2" href="cic:/fakeuri.def(1)"\snd/a p) then a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{a title="pair pi1" href="cic:/fakeuri.def(1)"\fst/a p} a title="union" href="cic:/fakeuri.def(1)"∪/a a title="singleton" href="cic:/fakeuri.def(1)"{/aa title="epsilon" href="cic:/fakeuri.def(1)"ϵ/a} else a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{a title="pair pi1" href="cic:/fakeuri.def(1)"\fst/a p}.
+img class="anchor" src="icons/tick.png" id="in_prl"definition in_prl ≝ λS : a href="cic:/matita/tutorial/chapter4/DeqSet.ind(1,0,0)"DeqSet/a.λp:a href="cic:/matita/tutorial/chapter7/pre.def(1)"pre/a S. 
+  if (a title="pair pi2" href="cic:/fakeuri.def(1)"\snd/a p) then a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{a title="pair pi1" href="cic:/fakeuri.def(1)"\fst/a pa title="in_pl" href="cic:/fakeuri.def(1)"}/a a title="union" href="cic:/fakeuri.def(1)"∪/a a title="singleton" href="cic:/fakeuri.def(1)"{/aa title="epsilon" href="cic:/fakeuri.def(1)"ϵ/aa title="singleton" href="cic:/fakeuri.def(1)"}/a else a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{a title="pair pi1" href="cic:/fakeuri.def(1)"\fst/a pa title="in_pl" href="cic:/fakeuri.def(1)"}/a.
   
 interpretation "in_prl mem" 'mem w l = (in_prl ? l w).
 interpretation "in_prl" 'in_l E = (in_prl ? E).
 
 (* The following, trivial lemmas are only meant for rewriting purposes. *)
 
-lemma sem_pre_true : ∀S.∀i:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S. 
-  a title="in_prl" href="cic:/fakeuri.def(1)"\sem/a{a title="Pair construction" href="cic:/fakeuri.def(1)"〈/ai,a href="cic:/matita/basics/bool/bool.con(0,1,0)"true/a〉} a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i} a title="union" href="cic:/fakeuri.def(1)"∪/a a title="singleton" href="cic:/fakeuri.def(1)"{/aa title="epsilon" href="cic:/fakeuri.def(1)"ϵ/a}. 
+img class="anchor" src="icons/tick.png" id="sem_pre_true"lemma sem_pre_true : ∀S.∀i:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S. 
+  a title="in_prl" href="cic:/fakeuri.def(1)"\sem/a{a title="Pair construction" href="cic:/fakeuri.def(1)"〈/ai,a href="cic:/matita/basics/bool/bool.con(0,1,0)"true/aa title="Pair construction" href="cic:/fakeuri.def(1)"〉/aa title="in_prl" href="cic:/fakeuri.def(1)"}/a a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{ia title="in_pl" href="cic:/fakeuri.def(1)"}/a a title="union" href="cic:/fakeuri.def(1)"∪/a a title="singleton" href="cic:/fakeuri.def(1)"{/aa title="epsilon" href="cic:/fakeuri.def(1)"ϵ/aa title="singleton" href="cic:/fakeuri.def(1)"}/a. 
 // qed.
 
-lemma sem_pre_false : ∀S.∀i:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S. 
-  a title="in_prl" href="cic:/fakeuri.def(1)"\sem/a{a title="Pair construction" href="cic:/fakeuri.def(1)"〈/ai,a href="cic:/matita/basics/bool/bool.con(0,2,0)"false/a〉} a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i}. 
+img class="anchor" src="icons/tick.png" id="sem_pre_false"lemma sem_pre_false : ∀S.∀i:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S. 
+  a title="in_prl" href="cic:/fakeuri.def(1)"\sem/a{a title="Pair construction" href="cic:/fakeuri.def(1)"〈/ai,a href="cic:/matita/basics/bool/bool.con(0,2,0)"false/aa title="Pair construction" href="cic:/fakeuri.def(1)"〉/aa title="in_prl" href="cic:/fakeuri.def(1)"}/a a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{ia title="in_pl" href="cic:/fakeuri.def(1)"}/a. 
 // qed.
 
-lemma sem_cat: ∀S.∀i1,i2:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S. 
-  a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i1 a title="pitem cat" href="cic:/fakeuri.def(1)"·/a i2} a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i1} a title="cat lang" href="cic:/fakeuri.def(1)"·/a a title="in_l" href="cic:/fakeuri.def(1)"\sem/a{a title="forget" href="cic:/fakeuri.def(1)"|/ai2|} a title="union" href="cic:/fakeuri.def(1)"∪/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i2}.
+img class="anchor" src="icons/tick.png" id="sem_cat"lemma sem_cat: ∀S.∀i1,i2:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S. 
+  a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i1 a title="pitem cat" href="cic:/fakeuri.def(1)"·/a i2a title="in_pl" href="cic:/fakeuri.def(1)"}/a a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i1a title="in_pl" href="cic:/fakeuri.def(1)"}/a a title="cat lang" href="cic:/fakeuri.def(1)"·/a a title="in_l" href="cic:/fakeuri.def(1)"\sem/a{a title="forget" href="cic:/fakeuri.def(1)"|/ai2a title="forget" href="cic:/fakeuri.def(1)"|/aa title="in_l" href="cic:/fakeuri.def(1)"}/a a title="union" href="cic:/fakeuri.def(1)"∪/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i2a title="in_pl" href="cic:/fakeuri.def(1)"}/a.
 // qed.
 
-lemma sem_cat_w: ∀S.∀i1,i2:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S.∀w.
-  a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i1 a title="pitem cat" href="cic:/fakeuri.def(1)"·/a i2} w a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a ((a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i1} a title="cat lang" href="cic:/fakeuri.def(1)"·/a a title="in_l" href="cic:/fakeuri.def(1)"\sem/a{a title="forget" href="cic:/fakeuri.def(1)"|/ai2|}) w a title="logical or" href="cic:/fakeuri.def(1)"∨/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i2} w).
+img class="anchor" src="icons/tick.png" id="sem_cat_w"lemma sem_cat_w: ∀S.∀i1,i2:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S.∀w.
+  a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i1 a title="pitem cat" href="cic:/fakeuri.def(1)"·/a i2a title="in_pl" href="cic:/fakeuri.def(1)"}/a w a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a ((a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i1a title="in_pl" href="cic:/fakeuri.def(1)"}/a a title="cat lang" href="cic:/fakeuri.def(1)"·/a a title="in_l" href="cic:/fakeuri.def(1)"\sem/a{a title="forget" href="cic:/fakeuri.def(1)"|/ai2a title="forget" href="cic:/fakeuri.def(1)"|/aa title="in_l" href="cic:/fakeuri.def(1)"}/a) w a title="logical or" href="cic:/fakeuri.def(1)"∨/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i2a title="in_pl" href="cic:/fakeuri.def(1)"}/a w).
 // qed.
 
-lemma sem_plus: ∀S.∀i1,i2:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S. 
-  a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i1 a title="pitem or" href="cic:/fakeuri.def(1)"+/a i2} a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i1} a title="union" href="cic:/fakeuri.def(1)"∪/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i2}.
+img class="anchor" src="icons/tick.png" id="sem_plus"lemma sem_plus: ∀S.∀i1,i2:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S. 
+  a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i1 a title="pitem or" href="cic:/fakeuri.def(1)"+/a i2a title="in_pl" href="cic:/fakeuri.def(1)"}/a a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i1a title="in_pl" href="cic:/fakeuri.def(1)"}/a a title="union" href="cic:/fakeuri.def(1)"∪/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i2a title="in_pl" href="cic:/fakeuri.def(1)"}/a.
 // qed.
 
-lemma sem_plus_w: ∀S.∀i1,i2:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S.∀w. 
-  a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i1 a title="pitem or" href="cic:/fakeuri.def(1)"+/a i2} w a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a (a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i1} w a title="logical or" href="cic:/fakeuri.def(1)"∨/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i2} w).
+img class="anchor" src="icons/tick.png" id="sem_plus_w"lemma sem_plus_w: ∀S.∀i1,i2:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S.∀w. 
+  a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i1 a title="pitem or" href="cic:/fakeuri.def(1)"+/a i2a title="in_pl" href="cic:/fakeuri.def(1)"}/a w a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a (a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i1a title="in_pl" href="cic:/fakeuri.def(1)"}/a w a title="logical or" href="cic:/fakeuri.def(1)"∨/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i2a title="in_pl" href="cic:/fakeuri.def(1)"}/a w).
 // qed.
 
-lemma sem_star : ∀S.∀i:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S.
-  a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{ia title="pitem star" href="cic:/fakeuri.def(1)"^/a*} a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i} a title="cat lang" href="cic:/fakeuri.def(1)"·/a a title="in_l" href="cic:/fakeuri.def(1)"\sem/a{a title="forget" href="cic:/fakeuri.def(1)"|/ai|}a title="star lang" href="cic:/fakeuri.def(1)"^/a*.
+img class="anchor" src="icons/tick.png" id="sem_star"lemma sem_star : ∀S.∀i:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S.
+  a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{ia title="pitem star" href="cic:/fakeuri.def(1)"^/aa title="pitem star" href="cic:/fakeuri.def(1)"*/aa title="in_pl" href="cic:/fakeuri.def(1)"}/a a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{ia title="in_pl" href="cic:/fakeuri.def(1)"}/a a title="cat lang" href="cic:/fakeuri.def(1)"·/a a title="in_l" href="cic:/fakeuri.def(1)"\sem/a{a title="forget" href="cic:/fakeuri.def(1)"|/aia title="forget" href="cic:/fakeuri.def(1)"|/aa title="in_l" href="cic:/fakeuri.def(1)"}/aa title="star lang" href="cic:/fakeuri.def(1)"^/aa title="star lang" href="cic:/fakeuri.def(1)"*/a.
 // qed.
 
-lemma sem_star_w : ∀S.∀i:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S.∀w.
-  a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{ia title="pitem star" href="cic:/fakeuri.def(1)"^/a*} w a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a (a title="exists" href="cic:/fakeuri.def(1)"∃/aw1,w2.w1 a title="append" href="cic:/fakeuri.def(1)"@/a w2 a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a w a title="logical and" href="cic:/fakeuri.def(1)"∧/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i} w1 a title="logical and" href="cic:/fakeuri.def(1)"∧/a a title="in_l" href="cic:/fakeuri.def(1)"\sem/a{a title="forget" href="cic:/fakeuri.def(1)"|/ai|}a title="star lang" href="cic:/fakeuri.def(1)"^/a* w2).
+img class="anchor" src="icons/tick.png" id="sem_star_w"lemma sem_star_w : ∀S.∀i:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S.∀w.
+  a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{ia title="pitem star" href="cic:/fakeuri.def(1)"^/aa title="pitem star" href="cic:/fakeuri.def(1)"*/aa title="in_pl" href="cic:/fakeuri.def(1)"}/a w a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a (a title="exists" href="cic:/fakeuri.def(1)"∃/aw1,w2a title="exists" href="cic:/fakeuri.def(1)"./aw1 a title="append" href="cic:/fakeuri.def(1)"@/a w2 a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a w a title="logical and" href="cic:/fakeuri.def(1)"∧/a a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{ia title="in_pl" href="cic:/fakeuri.def(1)"}/a w1 a title="logical and" href="cic:/fakeuri.def(1)"∧/a a title="in_l" href="cic:/fakeuri.def(1)"\sem/a{a title="forget" href="cic:/fakeuri.def(1)"|/aia title="forget" href="cic:/fakeuri.def(1)"|/aa title="in_l" href="cic:/fakeuri.def(1)"}/aa title="star lang" href="cic:/fakeuri.def(1)"^/aa title="star lang" href="cic:/fakeuri.def(1)"*/a w2).
 // qed.
 
 (* Below are a few, simple, semantic properties of items. In particular:
@@ -268,10 +268,10 @@ lemma sem_star_w : ∀S.∀i:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,
 The first property is proved by a simple induction on $i$; the other
 results are easy corollaries. We need an auxiliary lemma first. *)
 
-lemma append_eq_nil : ∀S.∀w1,w2:a href="cic:/matita/tutorial/chapter6/word.def(3)"word/a S. w1 a title="append" href="cic:/fakeuri.def(1)"@/a w2 a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="epsilon" href="cic:/fakeuri.def(1)"ϵ/a → w1 a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="epsilon" href="cic:/fakeuri.def(1)"ϵ/a.
+img class="anchor" src="icons/tick.png" id="append_eq_nil"lemma append_eq_nil : ∀S.∀w1,w2:a href="cic:/matita/tutorial/chapter6/word.def(3)"word/a S. w1 a title="append" href="cic:/fakeuri.def(1)"@/a w2 a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="epsilon" href="cic:/fakeuri.def(1)"ϵ/a → w1 a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a title="epsilon" href="cic:/fakeuri.def(1)"ϵ/a.
 #S #w1 #w2 cases w1 // #a #tl normalize #H destruct qed.
 
-lemma not_epsilon_lp : ∀S:a href="cic:/matita/tutorial/chapter4/DeqSet.ind(1,0,0)"DeqSet/a.∀e:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S. a title="logical not" href="cic:/fakeuri.def(1)"¬/a (a title="epsilon" href="cic:/fakeuri.def(1)"ϵ/a a title="in_pl mem" href="cic:/fakeuri.def(1)"∈/a e).
+img class="anchor" src="icons/tick.png" id="not_epsilon_lp"lemma not_epsilon_lp : ∀S:a href="cic:/matita/tutorial/chapter4/DeqSet.ind(1,0,0)"DeqSet/a.∀e:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S. a title="logical not" href="cic:/fakeuri.def(1)"¬/a (a title="epsilon" href="cic:/fakeuri.def(1)"ϵ/a a title="in_pl mem" href="cic:/fakeuri.def(1)"∈/a e).
 #S #e elim e normalize /span class="autotactic"2span class="autotrace" trace a href="cic:/matita/basics/logic/Not.con(0,1,1)"nmk/a/span/span/  
   [#r1 #r2 * #n1 #n2 % * /span class="autotactic"2span class="autotrace" trace a href="cic:/matita/basics/logic/absurd.def(2)"absurd/a/span/span/ * #w1 * #w2 * * #H 
    >(a href="cic:/matita/tutorial/chapter7/append_eq_nil.def(4)"append_eq_nil/a …H…) /span class="autotactic"2span class="autotrace" trace /span/span/
@@ -280,22 +280,22 @@ lemma not_epsilon_lp : ∀S:a href="cic:/matita/tutorial/chapter4/DeqSet.ind(1,
   ]
 qed.
 
-lemma epsilon_to_true : ∀S.∀e:a href="cic:/matita/tutorial/chapter7/pre.def(1)"pre/a S. a title="epsilon" href="cic:/fakeuri.def(1)"ϵ/a a title="in_prl mem" href="cic:/fakeuri.def(1)"∈/a e → a title="pair pi2" href="cic:/fakeuri.def(1)"\snd/a e a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a href="cic:/matita/basics/bool/bool.con(0,1,0)"true/a.
+img class="anchor" src="icons/tick.png" id="epsilon_to_true"lemma epsilon_to_true : ∀S.∀e:a href="cic:/matita/tutorial/chapter7/pre.def(1)"pre/a S. a title="epsilon" href="cic:/fakeuri.def(1)"ϵ/a a title="in_prl mem" href="cic:/fakeuri.def(1)"∈/a e → a title="pair pi2" href="cic:/fakeuri.def(1)"\snd/a e a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a href="cic:/matita/basics/bool/bool.con(0,1,0)"true/a.
 #S * #i #b cases b // normalize #H @a href="cic:/matita/basics/logic/False_ind.fix(0,1,1)"False_ind/a /span class="autotactic"2span class="autotrace" trace a href="cic:/matita/basics/logic/absurd.def(2)"absurd/a/span/span/ 
 qed.
 
-lemma true_to_epsilon : ∀S.∀e:a href="cic:/matita/tutorial/chapter7/pre.def(1)"pre/a S. a title="pair pi2" href="cic:/fakeuri.def(1)"\snd/a e a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a href="cic:/matita/basics/bool/bool.con(0,1,0)"true/a → a title="epsilon" href="cic:/fakeuri.def(1)"ϵ/a a title="in_prl mem" href="cic:/fakeuri.def(1)"∈/a e.
+img class="anchor" src="icons/tick.png" id="true_to_epsilon"lemma true_to_epsilon : ∀S.∀e:a href="cic:/matita/tutorial/chapter7/pre.def(1)"pre/a S. a title="pair pi2" href="cic:/fakeuri.def(1)"\snd/a e a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a a href="cic:/matita/basics/bool/bool.con(0,1,0)"true/a → a title="epsilon" href="cic:/fakeuri.def(1)"ϵ/a a title="in_prl mem" href="cic:/fakeuri.def(1)"∈/a e.
 #S * #i #b #btrue normalize in btrue; >btrue %2 // 
 qed.
 
-lemma minus_eps_item: ∀S.∀i:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S. a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i} a title="extensional equality" href="cic:/fakeuri.def(1)"=/a1 a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{i}a title="substraction" href="cic:/fakeuri.def(1)"-/aa title="singleton" href="cic:/fakeuri.def(1)"{/aa title="nil" href="cic:/fakeuri.def(1)"[/a ]}.
+img class="anchor" src="icons/tick.png" id="minus_eps_item"lemma minus_eps_item: ∀S.∀i:a href="cic:/matita/tutorial/chapter7/pitem.ind(1,0,1)"pitem/a S. a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{ia title="in_pl" href="cic:/fakeuri.def(1)"}/a a title="extensional equality" href="cic:/fakeuri.def(1)"=/a1 a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{ia title="in_pl" href="cic:/fakeuri.def(1)"}/aa title="substraction" href="cic:/fakeuri.def(1)"-/aa title="singleton" href="cic:/fakeuri.def(1)"{/aa title="nil" href="cic:/fakeuri.def(1)"[/a a title="nil" href="cic:/fakeuri.def(1)"]/aa title="singleton" href="cic:/fakeuri.def(1)"}/a.
 #S #i #w % 
   [#H whd % // normalize @(a href="cic:/matita/basics/logic/not_to_not.def(3)"not_to_not/a … (a href="cic:/matita/tutorial/chapter7/not_epsilon_lp.def(8)"not_epsilon_lp/a …i)) //
   |* //
   ]
 qed.
 
-lemma minus_eps_pre: ∀S.∀e:a href="cic:/matita/tutorial/chapter7/pre.def(1)"pre/a S. a title="in_pl" href="cic:/fakeuri.def(1)"\sem/a{a title="pair pi1" href="cic:/fakeuri.def(1)"\fst/a e} a title="extensional equality" href="cic:/fakeuri.def(1)"=/a1 a title="in_prl" href="cic:/fakeuri.def(1)"\sem/a{e}a title="substraction" href="cic:/fakeuri.def(1)"-/aa title="singleton" href="cic:/fakeuri.def(1)"{/aa title="nil" href="cic:/fakeuri.def(1)"[/a ]}.
+img class="anchor" src="icons/tick.png" id="minus_eps_pre"lemma minus_eps_pre: ∀S.∀e:a href="cic:/matita/tutorial/chapter7/pre.def(1)"pre/a S. a title="in_pl" href="cic:/fakeuri.def(1)"\sem/aspan class="error" title="Parse error: [sym{] expected after [sym\sem ] (in [term])"/span{a title="pair pi1" href="cic:/fakeuri.def(1)"\fst/a ea title="in_pl" href="cic:/fakeuri.def(1)"}/a a title="extensional equality" href="cic:/fakeuri.def(1)"=/a1 a title="in_prl" href="cic:/fakeuri.def(1)"\sem/a{ea title="in_prl" href="cic:/fakeuri.def(1)"}/aa title="substraction" href="cic:/fakeuri.def(1)"-/aa title="singleton" href="cic:/fakeuri.def(1)"{/aa title="nil" href="cic:/fakeuri.def(1)"[/a a title="nil" href="cic:/fakeuri.def(1)"]/aa title="singleton" href="cic:/fakeuri.def(1)"}/a.
 #S * #i * 
   [>a href="cic:/matita/tutorial/chapter7/sem_pre_true.def(9)"sem_pre_true/a normalize in ⊢ (??%?); #w % 
     [/span class="autotactic"3span class="autotrace" trace a href="cic:/matita/basics/logic/Or.con(0,1,2)"or_introl/a, a href="cic:/matita/basics/logic/And.con(0,1,2)"conj/a, a href="cic:/matita/basics/logic/not_to_not.def(3)"not_to_not/a/span/span/ | * * // #H1 #H2 @a href="cic:/matita/basics/logic/False_ind.fix(0,1,1)"False_ind/a @(a href="cic:/matita/basics/logic/absurd.def(2)"absurd/a …H1 H2)]