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<b>let </b><font color="Maroon" title="c1">G1</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"> for <font color="Olive" title="b1">G2</font> being <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a>  <a href="glib_000.html#M2" title="GLIB_000:mode.2">Subgraph</a> of <font color="Maroon" title="c1">G1</font>  st <font color="Olive" title="b1">G2</font> is <a href="glib_000.html#V9" title="GLIB_000:attr.9">spanning</a> holds <br/><font color="Maroon" title="c1">G1</font> is <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a></span><br/><b>let </b><font color="Maroon" title="c2">G2</font> be  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a>  <a href="glib_000.html#M2" title="GLIB_000:mode.2">Subgraph</a> of <font color="Maroon" title="c1">G1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V9" title="GLIB_000:attr.9">spanning</a> implies <font color="Maroon" title="c1">G1</font> is <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> )</span><br/>



<b>assume </b><a NAME="E1:37"/><i><font color="Green" title="E22">A1</font></i>: 
<font color="Maroon" title="c2">G2</font> is <a href="glib_000.html#V9" title="GLIB_000:attr.9">spanning</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">G1</font> is <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">u'</font>, <font color="Maroon" title="c4">v'</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</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">G1</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">u'</font>,<font color="Maroon" title="c4">v'</font></span><br/><b>reconsider </b><font color="Maroon" title="c5">u</font> = <font color="Maroon" title="c3">u'</font>, <font color="Maroon" title="c6">v</font> = <font color="Maroon" title="c4">v'</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font> <b>by </b><i><a class="txt" href="#E1:37"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="glib_000.html#D35" title="GLIB_000:def.35">GLIB_000:def 35</a></i>;<br/><b>consider </b><font color="Maroon" title="c7">W</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c2">G2</font><b> such that </b><br/><a NAME="E3:37_1"/><i><font color="Green" title="E23">A2</font></i>: 
<font color="Maroon" title="c7">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c6">v</font>
 <b>by </b><i><a class="ref" href="glib_002.html#D1" target="_self" title="GLIB_002:def.1">Def1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c8">W</font> = <font color="Maroon" title="c7">W</font> as    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G1</font> <b>by </b><i><a class="ref" href="glib_001.html#T168" title="GLIB_001:th.168">GLIB_001:168</a></i>;<br/><b>take </b><font color="Maroon" title="c9">W</font> = <font color="Maroon" title="c8">W</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c3">u'</font>,<font color="Maroon" title="c4">v'</font></span><br/><b>thus </b><a NAME="E5:37_1"/>
<font color="Maroon" title="c9">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c3">u'</font>,<font color="Maroon" title="c4">v'</font>
 <b>by </b><i><a class="txt" href="#E3:37_1"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="glib_001.html#T20" title="GLIB_001:th.20">GLIB_001:20</a></i>; <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="E3:37"/>
<font color="Maroon" title="c1">G1</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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