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: *)
-(* The fact of being able to decide, via a computable boolean function, the
+(*
+\ 5h1 class="section"\ 5Effective searching/h1\ 6
+The fact of being able to decide, via a computable boolean function, the
equality between elements of a given set is an essential prerequisite for
effectively searching an element of that set inside a data structure. In this
section we shall define several boolean functions acting on lists of elements in