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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  ex <font color="Olive" title="b1">v</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> st <font color="Maroon" title="c1">G</font> <a href="glib_002.html#K1" title="GLIB_002:func.1">.reachableFrom</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font> implies <font color="Maroon" title="c1">G</font> is <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> )</span><br/>

<b>assume </b><a NAME="E1:34"/>
 ex <font color="Olive" title="b1">v</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> st <font color="Maroon" title="c1">G</font> <a href="glib_002.html#K1" title="GLIB_002:func.1">.reachableFrom</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">G</font> is <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a></span><br/>

<b>then consider </b><font color="Maroon" title="c2">v</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E3:34"/><i><font color="Green" title="E19">A1</font></i>: 
<font color="Maroon" title="c1">G</font> <a href="glib_002.html#K1" title="GLIB_002:func.1">.reachableFrom</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font>
 ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">W</font> being   <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="c3">x</font>,<font color="Maroon" title="c4">y</font></span><br/><b>consider </b><font color="Maroon" title="c5">W1</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E2:34_1"/><i><font color="Green" title="E20">A2</font></i>: 
<font color="Maroon" title="c5">W1</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="c3">x</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E3:34"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="glib_002.html#D5" target="_self" title="GLIB_002:def.5">Def5</a></i>;<br/><b>consider </b><font color="Maroon" title="c6">W2</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E4:34_1"/><i><font color="Green" title="E21">A3</font></i>: 
<font color="Maroon" title="c6">W2</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="c4">y</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E3:34"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="glib_002.html#D5" target="_self" title="GLIB_002:def.5">Def5</a></i>;<br/><a NAME="E5:34_1"/>
<font color="Maroon" title="c5">W1</font> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a>  <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">v</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E2:34_1"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="glib_001.html#T24" title="GLIB_001:th.24">GLIB_001:24</a></i>;<br/><a NAME="E6:34_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">W1</font> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c6">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E4:34_1"><i><font color="Green" title="E21">A3</font></i></a>, <a class="ref" href="glib_001.html#T32" title="GLIB_001:th.32">GLIB_001:32</a></i>;<br/><b>hence </b><a NAME="E7:34_1"/>
 ex <font color="Olive" title="b1">W</font> being   <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="c3">x</font>,<font color="Maroon" title="c4">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:34"/>
<font color="Maroon" title="c1">G</font> is <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a>
 <b>by </b><i><a class="ref" href="glib_002.html#D1" target="_self" title="GLIB_002:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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