+ <para>It registers a cluster of related definitions and
+ theorems to be used by tactics and the rendering engine.
+ Some functionalities of Matita are not available when some
+ clusters have not been registered. Overloading a cluster
+ registration is possible: the last registration will be the
+ default one, but the previous ones are still in effect.</para>
+ <para>
+ <command>s</command> is an identifier of the cluster and
+ <command>u<subscript>1</subscript> … u<subscript>n</subscript></command>
+ are the URIs of the definitions and theorems of the cluster.
+ The number <command>n</command> of required URIs depends on the
+ cluster. The following clusters are supported.
+ </para>
+ <table>
+ <title>clusters</title>
+ <tgroup cols="6">
+ <thead>
+ <row>
+ <entry>name</entry>
+ <entry>expected object for 1st URI</entry>
+ <entry>expected object for 2nd URI</entry>
+ <entry>expected object for 3rd URI</entry>
+ <entry>expected object for 4th URI</entry>
+ <entry>expected object for 5th URI</entry>
+ <entry>expected object for 6th URI</entry>
+ <entry>expected object for 7th URI</entry>
+ <entry>expected object for 8th URI</entry>
+ <entry>expected object for 9th URI</entry>
+ <entry>expected object for 10th URI</entry>
+ <entry>expected object for 11th URI</entry>
+ </row>
+ </thead>
+ <tbody>
+ <row>
+ <entry>equality</entry>
+ <entry>an inductive type (say, of type <command>eq</command>) of type ∀A:Type.A <emphasis role="bold">→</emphasis> <emphasis role="bold">Prop</emphasis> with one family parameter and one constructor of type ∀x:A.eq A x</entry>
+ <entry>a theorem of type <emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>x,y:A.eq A x y <emphasis role="bold">→</emphasis> eq A y x</entry>
+ <entry>a theorem of type <emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>x,y,z:A.eq A x y <emphasis role="bold">→</emphasis> eq A y z <emphasis role="bold">→</emphasis> eq A x z</entry>
+ <entry><emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>a.<emphasis role="bold">∀</emphasis> P:A <emphasis role="bold">→</emphasis> <emphasis role="bold">Prop</emphasis>.P x <emphasis role="bold">→</emphasis> <emphasis role="bold">∀</emphasis>y.eq A x y <emphasis role="bold">→</emphasis> P y</entry>
+ <entry><emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>a.<emphasis role="bold">∀</emphasis> P:A <emphasis role="bold">→</emphasis> <emphasis role="bold">Prop</emphasis>.P x <emphasis role="bold">→</emphasis> <emphasis role="bold">∀</emphasis>y.eq A y x <emphasis role="bold">→</emphasis> P y</entry>
+ <entry><emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>a.<emphasis role="bold">∀</emphasis> P:A <emphasis role="bold">→</emphasis> <emphasis role="bold">Set</emphasis>.P x <emphasis role="bold">→</emphasis> <emphasis role="bold">∀</emphasis>y.eq A x y <emphasis role="bold">→</emphasis> P y</entry>
+ <entry><emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>a.<emphasis role="bold">∀</emphasis> P:A <emphasis role="bold">→</emphasis> <emphasis role="bold">Set</emphasis>.P x <emphasis role="bold">→</emphasis> <emphasis role="bold">∀</emphasis>y.eq A y x <emphasis role="bold">→</emphasis> P y</entry>
+ <entry><emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>a.<emphasis role="bold">∀</emphasis> P:A <emphasis role="bold">→</emphasis> <emphasis role="bold">Type</emphasis>.P x <emphasis role="bold">→</emphasis> <emphasis role="bold">∀</emphasis>y.eq A x y <emphasis role="bold">→</emphasis> P y</entry>
+ <entry><emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>a.<emphasis role="bold">∀</emphasis> P:A <emphasis role="bold">→</emphasis> <emphasis role="bold">Type</emphasis>.P x <emphasis role="bold">→</emphasis> <emphasis role="bold">∀</emphasis>y.eq A y x <emphasis role="bold">→</emphasis> P y</entry>
+ <entry><emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>B.<emphasis role="bold">∀</emphasis> f:A <emphasis role="bold">→</emphasis> B.<emphasis role="bold">∀</emphasis>x,y:A.eq A x y <emphasis role="bold">→</emphasis> eq B (f x) (f y)</entry>
+ <entry><emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>B.<emphasis role="bold">∀</emphasis> f:A <emphasis role="bold">→</emphasis> B.<emphasis role="bold">∀</emphasis>x,y:A.eq A x y <emphasis role="bold">→</emphasis> eq B (f y) (f x)</entry>
+ </row>
+ <row>
+ <entry>true</entry>
+ <entry>an inductive type of type <emphasis role="bold">Prop</emphasis> with only one constructor that has no arguments</entry>
+ <entry/>
+ <entry/>
+ <entry/>
+ <entry/>
+ </row>
+ <row>
+ <entry>false</entry>
+ <entry>an inductive type of type <emphasis role="bold">Prop</emphasis> without constructors</entry>
+ <entry/>
+ <entry/>
+ <entry/>
+ <entry/>
+ </row>
+ <row>
+ <entry>absurd</entry>
+ <entry>a theorem of type <emphasis role="bold">∀</emphasis>A:Prop.<emphasis role="bold">∀</emphasis>B:Prop.A <emphasis role="bold">→</emphasis> Not A <emphasis role="bold">→</emphasis> B</entry>
+ <entry/>
+ <entry/>
+ <entry/>
+ <entry/>
+ </row>
+ </tbody>
+ </tgroup>
+ </table>