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<b>let </b><font color="Maroon" title="c3">IT1</font>, <font color="Maroon" title="c4">IT2</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:17_1_2"/><i><font color="Green" title="E7">A3</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">IT1</font> iff  ex <font color="Olive" title="b2">W</font> being <a href="glib_001.html#V2" title="GLIB_001:attr.2">directed</a>  <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font> st <font color="Olive" title="b2">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">v</font>,<font color="Olive" title="b1">x</font> )
 <b>and </b><br/><a NAME="E2:17_1_2"/><i><font color="Green" title="E8">A4</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">IT2</font> iff  ex <font color="Olive" title="b2">W</font> being <a href="glib_001.html#V2" title="GLIB_001:attr.2">directed</a>  <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font> st <font color="Olive" title="b2">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">v</font>,<font color="Olive" title="b1">x</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:17_1_2_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">IT1</font>
 ;<br/><a NAME="E2:17_1_2_1_1"/><b>then </b>
 ex <font color="Olive" title="b1">W</font> being <a href="glib_001.html#V2" title="GLIB_001:attr.2">directed</a>  <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font> st <font color="Olive" title="b1">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E1:17_1_2"><i><font color="Green" title="E7">A3</font></i></a></i>;<br/><b>hence </b><a NAME="E3:17_1_2_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">IT2</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E2:17_1_2"><i><font color="Green" title="E8">A4</font></i></a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:17_1_2_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">IT2</font>
 ;<br/><a NAME="E3:17_1_2_1"/><b>then </b>
 ex <font color="Olive" title="b1">W</font> being <a href="glib_001.html#V2" title="GLIB_001:attr.2">directed</a>  <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font> st <font color="Olive" title="b1">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E2:17_1_2"><i><font color="Green" title="E8">A4</font></i></a></i>;<br/><b>hence </b><a NAME="E4:17_1_2_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">IT1</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E1:17_1_2"><i><font color="Green" title="E7">A3</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:17_1_2"/>
<font color="Maroon" title="c3">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">IT2</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></i>;<br/>


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