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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:20"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="glib_002.html#K1" target="_self">.reachableFrom</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:20"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="glib_002.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E4:20"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="glib_001.html#K6">.reverse()</a>  <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="glib_002.html#E3:20"><i><font color="Green">E11</font></i></a>, <a class="ref" href="glib_001.html#T24">GLIB_001:24</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:20_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="glib_002.html#K1" target="_self">.reachableFrom</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:20_1_1"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="glib_002.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E4:20_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="glib_001.html#K7">.append</a> <font color="Maroon">c<sub>6</sub></font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="glib_002.html#E3:20"><i><font color="Green">E11</font></i></a>, <a class="txt" href="glib_002.html#E3:20_1_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="glib_001.html#T32">GLIB_001:32</a></i>;<br/><b>hence </b><a NAME="E5:20_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="glib_002.html#K1" target="_self">.reachableFrom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="glib_002.html#D5" target="_self">Def5</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:20_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="glib_002.html#K1" target="_self">.reachableFrom</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="glib_001.html#M3">Walk</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:20_1"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="glib_002.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E5:20_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="glib_001.html#K6">.reverse()</a> </span>)</span> <a href="glib_001.html#K7">.append</a> <font color="Maroon">c<sub>6</sub></font> <a href="glib_001.html#R1">is_Walk_from</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="glib_002.html#E4:20"><i><font color="Green">E12</font></i></a>, <a class="txt" href="glib_002.html#E4:20_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="glib_001.html#T32">GLIB_001:32</a></i>;<br/><b>hence </b><a NAME="E6:20_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="glib_002.html#K1" target="_self">.reachableFrom</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="glib_002.html#D5" target="_self">Def5</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:20"/>
<font color="Maroon">c<sub>1</sub></font> <a href="glib_002.html#K1" target="_self">.reachableFrom</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="glib_002.html#K1" target="_self">.reachableFrom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


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