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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b> ex <font color="Olive">v</font> being  <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font> st <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_002.html#K1" target="_self">.reachableFrom</a> <font color="Olive">v</font>;<br/>
<b>consider </b><font color="Maroon">IT</font> being   <a href="setfam_1.html#NM1">Subset-Family</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span><b> such that </b><br/><a NAME="E2:27_1_1"/><i><font color="Green">E41</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font> iff ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] ) )
 <b>from </b><i><a class="ref" href="subset_1.html#S1">SUBSET_1:sch 1</a>();<br/></i>
<b>consider </b><font color="Maroon">v</font> being   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font>;<br/>
<b>set </b><font color="Maroon">x</font> = <font color="Maroon">G</font> <a href="glib_002.html#K1" target="_self">.reachableFrom</a> <font color="Maroon">v</font>;<br/>
<a NAME="E4:27_1_1"/>
<font color="Maroon">G</font> <a href="glib_002.html#K1" target="_self">.reachableFrom</a> <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font>
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">IT</font> = <font color="Maroon">IT</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="setfam_1.html#NM1">Subset-Family</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> ;<br/>
<b>take </b>
<font color="Maroon">IT</font>
;<br/>

<b>thus </b><a NAME="E6:27_1_1"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font> iff  ex <font color="Olive">v</font> being  <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font> st <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_002.html#K1" target="_self">.reachableFrom</a> <font color="Olive">v</font> )
 <b>by </b><i/>;<br/>


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