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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_000.html#M2" title="GLIB_000:mode.2">Subgraph</a> of <font color="Maroon" title="c1">G1</font><br/> for <font color="Olive" title="b2">v1</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font><br/> for <font color="Olive" title="b3">v2</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Olive" title="b1">G2</font>  st <font color="Olive" title="b2">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v2</font> &amp; <font color="Olive" title="b2">v1</font> is <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a> holds <br/><font color="Olive" title="b3">v2</font> is <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a></span><br/><b>let </b><font color="Maroon" title="c2">G2</font> be    <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"> for <font color="Olive" title="b1">v1</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font><br/> for <font color="Olive" title="b2">v2</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font>  st <font color="Olive" title="b1">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v2</font> &amp; <font color="Olive" title="b1">v1</font> is <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a> holds <br/><font color="Olive" title="b2">v2</font> is <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a></span><br/><b>let </b><font color="Maroon" title="c3">v1</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"> for <font color="Olive" title="b1">v2</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font>  st <font color="Maroon" title="c3">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v2</font> &amp; <font color="Maroon" title="c3">v1</font> is <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a> holds <br/><font color="Olive" title="b1">v2</font> is <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a></span><br/><b>let </b><font color="Maroon" title="c4">v2</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v2</font> &amp; <font color="Maroon" title="c3">v1</font> is <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a> implies <font color="Maroon" title="c4">v2</font> is <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a> )</span><br/>







<b>assume </b><a NAME="E1:175"/>
( <font color="Maroon" title="c3">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v2</font> &amp; <font color="Maroon" title="c3">v1</font> is <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">v2</font> is <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a></span><br/>

<a NAME="E2:175"/><b>then </b>
( <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K29" title="GLIB_000:func.29">.edgesInOut()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K29" title="GLIB_000:func.29">.edgesInOut()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K29" title="GLIB_000:func.29">.edgesInOut()</a>  )
 
<b>by </b><i><a class="ref" href="glib_000.html#D51" target="_self" title="GLIB_000:def.51">Def51</a>, <a class="ref" href="glib_000.html#T81" target="_self" title="GLIB_000:th.81">Th81</a></i>;<br/>
<a NAME="E3:175"/><b>then </b>
<font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K29" title="GLIB_000:func.29">.edgesInOut()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
;<br/>
<b>hence </b><a NAME="E4:175"/>
<font color="Maroon" title="c4">v2</font> is <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a>
 <b>by </b><i><a class="ref" href="glib_000.html#D51" target="_self" title="GLIB_000:def.51">Def51</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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