Sectionin

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

diff --git a/weblib/tutorial/chapter4.ma b/weblib/tutorial/chapter4.ma
index 20762a99a25975239a42be90d10572eb063c24a1..32a3f23eaa596d83d75f801a7df4047678cea905 100644 (file)
--- a/weblib/tutorial/chapter4.ma
+++ b/weblib/tutorial/chapter4.ma
@@ -44,14 +44,16 @@ sets *)
 definition subset: ∀A:Type[0].∀P,Q:A→Prop.Prop ≝ λA,P,Q.∀a:A.(P a → Q a).
 interpretation "subset" 'subseteq a b = (subset ? a b).
 
-(* Two sets are equals if and only if they have the same elements, that is,
+(* \ 5h2 class="section"\ 6Set Quality\ 5/h2\ 6
+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\ 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).
 
-(* This notion of equality is different from the intensional equality of
+(*
+This notion of equality is different from the intensional equality of
 functions; the fact it defines an equivalence relation must be explicitly 
 proved: *)
 
@@ -225,7 +227,9 @@ DeqSet is decidable in the traditional sense, namely either a=b or a≠b *)
   [%1 @(\P H) | %2 @(\Pf H)]
 qed.
 
-(* A simple example of a set with a decidable equality is bool. We first define 
+(* 
+\ 5h2 class="section"\ 6Unification Hints\ 5/h2\ 6
+A simple example of a set with a decidable equality is bool. We first define 
 the boolean equality beqb, that is just the xand function, then prove that 
 beqb b1 b2 is true if and only if b1=b2, and finally build the type DeqBool by 
 instantiating the DeqSet record with the previous information *)
@@ -241,9 +245,7 @@ qed.
 
 definition DeqBool ≝ \ 5a href="cic:/matita/tutorial/chapter4/DeqSet.con(0,1,0)"\ 6mk_DeqSet\ 5/a\ 6 \ 5a href="cic:/matita/basics/bool/bool.ind(1,0,0)"\ 6bool\ 5/a\ 6 \ 5a href="cic:/matita/tutorial/chapter4/beqb.def(2)"\ 6beqb\ 5/a\ 6 \ 5a href="cic:/matita/tutorial/chapter4/beqb_true.def(4)"\ 6beqb_true\ 5/a\ 6.
 
-(* 
-\ 5h2 class="section"\ 6Unification Hints\ 5/h2\ 6
-At this point, we would expect to be able to prove things like the
+(* At this point, we would expect to be able to prove things like the
 following: for any boolean b, if b==false is true then b=false. 
 Unfortunately, this would not work, unless we declare b of type 
 DeqBool (change the type in the following statement and see what