commit by user andrea

[helm.git] / weblib / tutorial / chapter4.ma

diff --git a/weblib/tutorial/chapter4.ma b/weblib/tutorial/chapter4.ma
index 55e734d56a5fa36cf400dea83b04bd70040c6a15..be8ddaa594212f9b0dacba4a7d7ddb8c81a23982 100644 (file)
--- 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.x\ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6a.
+definition singleton ≝ λA.λx,a:A.x\ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6\ 5span class="error" title="Parse error: [term] expected after [sym=] (in [term])"\ 6\ 5/span\ 6a.
 (* 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 \ 5a title="logical or" href="cic:/fakeuri.def(1)"\ 6∨\ 5/a\ 6 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 \ 5a title="logical and" href="cic:/fakeuri.def(1)"\ 6∧\ 5/a\ 6 Q a.
+definition intersection : ∀A:Type[0].∀P,Q.A→Prop ≝ λA,P,Q,a.P a \ 5a title="logical and" href="cic:/fakeuri.def(1)"\ 6∧\ 5/a\ 6\ 5span class="error" title="Parse error: [term] expected after [sym∧] (in [term])"\ 6\ 5/span\ 6 Q a.
 interpretation "intersection" 'intersects a b = (intersection ? a b).
 
 definition complement ≝ λU:Type[0].λA:U → Prop.λw.\ 5a title="logical not" href="cic:/fakeuri.def(1)"\ 6¬\ 5/a\ 6 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 \ 5a title="iff" href="cic:/fakeuri.def(1)"\ 6↔\ 5/a\ 6 Q a.
+definition eqP ≝ λA:Type[0].λP,Q:A → Prop.∀a:A.P a \ 5a title="iff" href="cic:/fakeuri.def(1)"\ 6↔\ 5/a\ 6\ 5span class="error" title="Parse error: [term] expected after [sym↔] (in [term])"\ 6\ 5/span\ 6 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 \ 5a title="extensional equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 61 C  → A \ 5a title="union" href="cic:/fakeuri.def(1)"\ 6∪\ 5/a\ 6 B \ 5a title="extensional equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 61 C \ 5a title="union" href="cic:/fakeuri.def(1)"\ 6∪\ 5/a\ 6 B.
+  A \ 5a title="extensional equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6\ 5span class="error" title="Parse error: NUMBER '1' or [term] expected after [sym=] (in [term])"\ 6\ 5/span\ 61 C  → A \ 5a title="union" href="cic:/fakeuri.def(1)"\ 6∪\ 5/a\ 6 B \ 5a title="extensional equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 61 C \ 5a title="union" href="cic:/fakeuri.def(1)"\ 6∪\ 5/a\ 6 B.
 #U #A #B #C #eqAB #a @\ 5a href="cic:/matita/basics/logic/iff_or_r.def(2)"\ 6iff_or_r\ 5/a\ 6 @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 @\ 5a href="cic:/matita/basics/logic/iff_and_r.def(2)"\ 6iff_and_r\ 5/a\ 6 @eqAB qed.
   
 lemma eqP_intersect_l: ∀U.∀A,B,C:U →Prop. 
-  B \ 5a title="extensional equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 61 C  → A \ 5a title="intersection" href="cic:/fakeuri.def(1)"\ 6∩\ 5/a\ 6 B \ 5a title="extensional equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 61 A \ 5a title="intersection" href="cic:/fakeuri.def(1)"\ 6∩\ 5/a\ 6 C.
+  B \ 5a title="extensional equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 61 C  → A \ 5a title="intersection" href="cic:/fakeuri.def(1)"\ 6∩\ 5/a\ 6\ 5span class="error" title="Parse error: [term] expected after [sym∩] (in [term])"\ 6\ 5/span\ 6 B \ 5a title="extensional equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 61 A \ 5a title="intersection" href="cic:/fakeuri.def(1)"\ 6∩\ 5/a\ 6 C.
 #U #A #B #C #eqBC #a @\ 5a href="cic:/matita/basics/logic/iff_and_l.def(2)"\ 6iff_and_l\ 5/a\ 6 @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 \ 5a title="union" href="cic:/fakeuri.def(1)"\ 6∪\ 5/a\ 6 B \ 5a title="union" href="cic:/fakeuri.def(1)"\ 6∪\ 5/a\ 6 C \ 5a title="extensional equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 61 A \ 5a title="union" href="cic:/fakeuri.def(1)"\ 6∪\ 5/a\ 6 (B \ 5a title="union" href="cic:/fakeuri.def(1)"\ 6∪\ 5/a\ 6 C).
-#S #A #B #C #w % [* [* /\ 5span class="autotactic"\ 63\ 5span class="autotrace"\ 6 trace \ 5a href="cic:/matita/basics/logic/Or.con(0,1,2)"\ 6or_introl\ 5/a\ 6, \ 5a href="cic:/matita/basics/logic/Or.con(0,2,2)"\ 6or_intror\ 5/a\ 6\ 5/span\ 6\ 5/span\ 6/ | /\ 5span class="autotactic"\ 63\ 5span class="autotrace"\ 6 trace \ 5a href="cic:/matita/basics/logic/Or.con(0,2,2)"\ 6or_intror\ 5/a\ 6\ 5/span\ 6\ 5/span\ 6/] | * [/\ 5span class="autotactic"\ 63\ 5span class="autotrace"\ 6 trace \ 5a href="cic:/matita/basics/logic/Or.con(0,1,2)"\ 6or_introl\ 5/a\ 6\ 5/span\ 6\ 5/span\ 6/ | * /\ 5span class="autotactic"\ 63\ 5span class="autotrace"\ 6 trace \ 5a href="cic:/matita/basics/logic/Or.con(0,1,2)"\ 6or_introl\ 5/a\ 6, \ 5a href="cic:/matita/basics/logic/Or.con(0,2,2)"\ 6or_intror\ 5/a\ 6\ 5/span\ 6\ 5/span\ 6/]
+#S #A #B #C #w % [* [* /\ 5span class="autotactic"\ 63\ 5span class="autotrace"\ 6 trace \ 5a href="cic:/matita/basics/logic/Or.con(0,1,2)"\ 6or_introl\ 5/a\ 6, \ 5a href="cic:/matita/basics/logic/Or.con(0,2,2)"\ 6or_intror\ 5/a\ 6\ 5/span\ 6\ 5/span\ 6/ | /\ 5span class="autotactic"\ 63\ 5span class="autotrace"\ 6 trace \ 5a href="cic:/matita/basics/logic/Or.con(0,1,2)"\ 6or_introl\ 5/a\ 6, \ 5a href="cic:/matita/basics/logic/Or.con(0,2,2)"\ 6or_intror\ 5/a\ 6\ 5/span\ 6\ 5/span\ 6/ ] | * [/\ 5span class="autotactic"\ 63\ 5span class="autotrace"\ 6 trace \ 5a href="cic:/matita/basics/logic/Or.con(0,1,2)"\ 6or_introl\ 5/a\ 6\ 5/span\ 6\ 5/span\ 6/ | * /\ 5span class="autotactic"\ 63\ 5span class="autotrace"\ 6 trace \ 5a href="cic:/matita/basics/logic/Or.con(0,1,2)"\ 6or_introl\ 5/a\ 6, \ 5a href="cic:/matita/basics/logic/Or.con(0,2,2)"\ 6or_intror\ 5/a\ 6\ 5/span\ 6\ 5/span\ 6/]
 qed.   
 
 (* In the same way we prove commutativity and associativity for set