<?xml version="1.0"?>
<div class="add">

<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>let </b><font color="Maroon">IT1</font> be  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>, <font color="Maroon">IT2</font> be  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>assume </b><b>that </b><br/><a NAME="E1:27_1_2"/><i><font color="Green">E42</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">IT1</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] )
 <b>and </b><br/><a NAME="E2:27_1_2"/><i><font color="Green">E43</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">IT2</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><a NAME="E1:27_1_2_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT1</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">x</font>] )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E2:27_1_2_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT1</font> iff <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT2</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:27_1_2"/>
<font color="Maroon">IT1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">IT2</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


</div>
