X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=weblib%2Ftutorial%2Fchapter4.ma;h=be8ddaa594212f9b0dacba4a7d7ddb8c81a23982;hb=a2ba04cd90e76937720b16e37cb12a39b46181e3;hp=c159fa13db6b0dfe72246273c57a1db5ecab7236;hpb=bef004f9c2ab68f9f0f9c95536918681a61849fc;p=helm.git

diff --git a/weblib/tutorial/chapter4.ma b/weblib/tutorial/chapter4.ma
index c159fa13d..be8ddaa59 100644
--- a/weblib/tutorial/chapter4.ma
+++ b/weblib/tutorial/chapter4.ma
@@ -14,7 +14,7 @@ interpretation "empty set" 'empty_set = (empty_set ?).
 (* Similarly, a singleton set contaning containing an element a, is defined
 by by the characteristic function asserting equality with a *)
 
-definition singleton ≝ λA.λx,a:A.xa title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/aa.
+definition singleton ≝ λA.λx,a:A.xa title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/aspan class="error" title="Parse error: [term] expected after [sym=] (in [term])"/spana.
 (* notation "{x}" non associative with precedence 90 for @{'sing_lang $x}. *)
 interpretation "singleton" 'singl x = (singleton ? x).
 
@@ -27,7 +27,7 @@ conjunction and negation *)
 definition union : ∀A:Type[0].∀P,Q.A → Prop ≝ λA,P,Q,a.P a a title="logical or" href="cic:/fakeuri.def(1)"∨/a Q a.
 interpretation "union" 'union a b = (union ? a b).
 
-definition intersection : ∀A:Type[0].∀P,Q.A→Prop ≝ λA,P,Q,a.P a a title="logical and" href="cic:/fakeuri.def(1)"∧/a Q a.
+definition intersection : ∀A:Type[0].∀P,Q.A→Prop ≝ λA,P,Q,a.P a a title="logical and" href="cic:/fakeuri.def(1)"∧/aspan class="error" title="Parse error: [term] expected after [sym∧] (in [term])"/span Q a.
 interpretation "intersection" 'intersects a b = (intersection ? a b).
 
 definition complement ≝ λU:Type[0].λA:U → Prop.λw.a title="logical not" href="cic:/fakeuri.def(1)"¬/a A w.
@@ -45,7 +45,7 @@ interpretation "subset" 'subseteq a b = (subset ? a b).
 (* Two sets are equals if and only if they have the same elements, that is,
 if the two characteristic functions are extensionally equivalent: *) 
 
-definition eqP ≝ λA:Type[0].λP,Q:A → Prop.∀a:A.P a a title="iff" href="cic:/fakeuri.def(1)"↔/a Q a.
+definition eqP ≝ λA:Type[0].λP,Q:A → Prop.∀a:A.P a a title="iff" href="cic:/fakeuri.def(1)"↔/aspan class="error" title="Parse error: [term] expected after [sym↔] (in [term])"/span Q a.
 notation "A =1 B" non associative with precedence 45 for @{'eqP $A $B}.
 interpretation "extensional equality" 'eqP a b = (eqP ? a b).
 
@@ -65,7 +65,7 @@ lemma eqP_trans: ∀U.∀A,B,C:U →Prop.
 with respect to eqP: *)
 
 lemma eqP_union_r: ∀U.∀A,B,C:U →Prop. 
-  A a title="extensional equality" href="cic:/fakeuri.def(1)"=/a1 C  → A a title="union" href="cic:/fakeuri.def(1)"∪/a B a title="extensional equality" href="cic:/fakeuri.def(1)"=/a1 C a title="union" href="cic:/fakeuri.def(1)"∪/a B.
+  A a title="extensional equality" href="cic:/fakeuri.def(1)"=/aspan class="error" title="Parse error: NUMBER '1' or [term] expected after [sym=] (in [term])"/span1 C  → A a title="union" href="cic:/fakeuri.def(1)"∪/a B a title="extensional equality" href="cic:/fakeuri.def(1)"=/a1 C a title="union" href="cic:/fakeuri.def(1)"∪/a B.
 #U #A #B #C #eqAB #a @a href="cic:/matita/basics/logic/iff_or_r.def(2)"iff_or_r/a @eqAB qed.
   
 lemma eqP_union_l: ∀U.∀A,B,C:U →Prop. 
@@ -77,7 +77,7 @@ lemma eqP_intersect_r: ∀U.∀A,B,C:U →Prop.
 #U #A #B #C #eqAB #a @a href="cic:/matita/basics/logic/iff_and_r.def(2)"iff_and_r/a @eqAB qed.
   
 lemma eqP_intersect_l: ∀U.∀A,B,C:U →Prop. 
-  B a title="extensional equality" href="cic:/fakeuri.def(1)"=/a1 C  → A a title="intersection" href="cic:/fakeuri.def(1)"∩/a B a title="extensional equality" href="cic:/fakeuri.def(1)"=/a1 A a title="intersection" href="cic:/fakeuri.def(1)"∩/a C.
+  B a title="extensional equality" href="cic:/fakeuri.def(1)"=/a1 C  → A a title="intersection" href="cic:/fakeuri.def(1)"∩/aspan class="error" title="Parse error: [term] expected after [sym∩] (in [term])"/span B a title="extensional equality" href="cic:/fakeuri.def(1)"=/a1 A a title="intersection" href="cic:/fakeuri.def(1)"∩/a C.
 #U #A #B #C #eqBC #a @a href="cic:/matita/basics/logic/iff_and_l.def(2)"iff_and_l/a @eqBC qed.
 
 lemma eqP_substract_r: ∀U.∀A,B,C:U →Prop. 
@@ -103,7 +103,7 @@ lemma union_comm : ∀U.∀A,B:U →Prop.
 
 lemma union_assoc: ∀U.∀A,B,C:U → Prop. 
   A a title="union" href="cic:/fakeuri.def(1)"∪/a B a title="union" href="cic:/fakeuri.def(1)"∪/a C a title="extensional equality" href="cic:/fakeuri.def(1)"=/a1 A a title="union" href="cic:/fakeuri.def(1)"∪/a (B a title="union" href="cic:/fakeuri.def(1)"∪/a C).
-#S #A #B #C #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/Or.con(0,2,2)"or_intror/a/span/span/ | /span class="autotactic"3span class="autotrace" trace a href="cic:/matita/basics/logic/Or.con(0,2,2)"or_intror/a/span/span/] | * [/span class="autotactic"3span class="autotrace" trace a href="cic:/matita/basics/logic/Or.con(0,1,2)"or_introl/a/span/span/ | * /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/Or.con(0,2,2)"or_intror/a/span/span/]
+#S #A #B #C #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/Or.con(0,2,2)"or_intror/a/span/span/ | /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/Or.con(0,2,2)"or_intror/a/span/span/ ] | * [/span class="autotactic"3span class="autotrace" trace a href="cic:/matita/basics/logic/Or.con(0,1,2)"or_introl/a/span/span/ | * /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/Or.con(0,2,2)"or_intror/a/span/span/]
 qed.   
 
 (* In the same way we prove commutativity and associativity for set 
@@ -283,36 +283,36 @@ this, we must as usual define the boolen equality function, and prove
 it correctly reflects propositional equality. *)
 
 definition eq_pairs ≝
-  λA,B:DeqSet.λp1,p2:A×B.(\fst p1 == \fst p2) ∧ (\snd p1 == \snd p2).
+  λA,B:a href="cic:/matita/tutorial/chapter4/DeqSet.ind(1,0,0)"DeqSet/a.λp1,p2:Aa title="Product" href="cic:/fakeuri.def(1)"×/aB.(a title="pair pi1" href="cic:/fakeuri.def(1)"\fst/a p1 a title="eqb" href="cic:/fakeuri.def(1)"=/a= a title="pair pi1" href="cic:/fakeuri.def(1)"\fst/a p2) a title="boolean and" href="cic:/fakeuri.def(1)"∧/a (a title="pair pi2" href="cic:/fakeuri.def(1)"\snd/a p1 a title="eqb" href="cic:/fakeuri.def(1)"=/a= a title="pair pi2" href="cic:/fakeuri.def(1)"\snd/a p2).
 
-lemma eq_pairs_true: ∀A,B:DeqSet.∀p1,p2:A×B.
-  eq_pairs A B p1 p2 = true ↔ p1 = p2.
+lemma eq_pairs_true: ∀A,B:a href="cic:/matita/tutorial/chapter4/DeqSet.ind(1,0,0)"DeqSet/a.∀p1,p2:Aa title="Product" href="cic:/fakeuri.def(1)"×/aB.
+  a href="cic:/matita/tutorial/chapter4/eq_pairs.def(4)"eq_pairs/a A B p1 p2 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="iff" href="cic:/fakeuri.def(1)"↔/a p1 a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/a p2.
 #A #B * #a1 #b1 * #a2 #b2 %
-  [#H cases (andb_true …H) normalize #eqa #eqb >(\P eqa) >(\P eqb) //
-  |#H destruct normalize >(\b (refl … a2)) >(\b (refl … b2)) //
+  [#H cases (a href="cic:/matita/basics/bool/andb_true.def(5)"andb_true/a …H) normalize #eqa #eqb >(\P eqa) >(\P eqb) //
+  |#H destruct normalize >(\b (a href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/a … a2)) >(\b (a href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/a … b2)) //
   ]
 qed.
 
-definition DeqProd ≝ λA,B:DeqSet.
-  mk_DeqSet (A×B) (eq_pairs A B) (eq_pairs_true A B).
+definition DeqProd ≝ λA,B:a href="cic:/matita/tutorial/chapter4/DeqSet.ind(1,0,0)"DeqSet/a.
+  a href="cic:/matita/tutorial/chapter4/DeqSet.con(0,1,0)"mk_DeqSet/a (Aa title="Product" href="cic:/fakeuri.def(1)"×/aB) (a href="cic:/matita/tutorial/chapter4/eq_pairs.def(4)"eq_pairs/a A B) (a href="cic:/matita/tutorial/chapter4/eq_pairs_true.def(6)"eq_pairs_true/a A B).
 
 (* Having an unification problem of the kind T1×T2 = carr X, what kind 
 of hint can we give to the system? We expect T1 to be the carrier of a
 DeqSet C1, T2 to be the carrier of a DeqSet C2, and X to be DeqProd C1 C2.
 This is expressed by the following hint: *)
 
-unification hint  0 ≔ C1,C2; 
-    T1 ≟ carr C1,
-    T2 ≟ carr C2,
-    X ≟ DeqProd C1 C2
+unification hint  0 a href="cic:/fakeuri.def(1)" title="hint_decl_Type1"≔/a C1,C2; 
+    T1 ≟ a href="cic:/matita/tutorial/chapter4/carr.fix(0,0,2)"carr/a C1,
+    T2 ≟ a href="cic:/matita/tutorial/chapter4/carr.fix(0,0,2)"carr/a C2,
+    X ≟ a href="cic:/matita/tutorial/chapter4/DeqProd.def(7)"DeqProd/a C1 C2
 (* ---------------------------------------- *) ⊢ 
-    T1×T2 ≡ carr X.
+    T1a title="Product" href="cic:/fakeuri.def(1)"×/aT2 ≡ a href="cic:/matita/tutorial/chapter4/carr.fix(0,0,2)"carr/a X.
 
-unification hint  0 ≔ T1,T2,p1,p2; 
-    X ≟ DeqProd T1 T2
+unification hint  0 a href="cic:/fakeuri.def(1)" title="hint_decl_Type0"≔/a T1,T2,p1,p2; 
+    X ≟ a href="cic:/matita/tutorial/chapter4/DeqProd.def(7)"DeqProd/a T1 T2
 (* ---------------------------------------- *) ⊢ 
-    eq_pairs T1 T2 p1 p2 ≡ eqb X p1 p2.
+    a href="cic:/matita/tutorial/chapter4/eq_pairs.def(4)"eq_pairs/a T1 T2 p1 p2 ≡ a href="cic:/matita/tutorial/chapter4/eqb.fix(0,0,3)"eqb/a X p1 p2.
 
 example hint2: ∀b1,b2. 
-  〈b1,true〉==〈false,b2〉=true → 〈b1,true〉=〈false,b2〉.
+  a title="Pair construction" href="cic:/fakeuri.def(1)"〈/ab1,a href="cic:/matita/basics/bool/bool.con(0,1,0)"true/a〉a title="eqb" href="cic:/fakeuri.def(1)"=/a=a title="Pair construction" href="cic:/fakeuri.def(1)"〈/aa href="cic:/matita/basics/bool/bool.con(0,2,0)"false/a,b2〉a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/aa href="cic:/matita/basics/bool/bool.con(0,1,0)"true/a → a title="Pair construction" href="cic:/fakeuri.def(1)"〈/ab1,a href="cic:/matita/basics/bool/bool.con(0,1,0)"true/a〉a title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/aa title="Pair construction" href="cic:/fakeuri.def(1)"〈/aa href="cic:/matita/basics/bool/bool.con(0,2,0)"false/a,b2〉.
 #b1 #b2 #H @(\P H).
\ No newline at end of file