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<b>let </b><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/>

<b>assume </b><a NAME="E1:40"/><i><font color="Green" title="E24">A1</font></i>: 
<font color="Maroon" title="c1">G1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">G2</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="40_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">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="E1:40_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G1</font> <a href="glib_002.html#K3" title="GLIB_002:func.3">.componentSet()</a> 
 ;<br/><b>then consider </b><font color="Maroon" title="c4">v1</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font><b> such that </b><br/><a NAME="E3:40_1_1"/><i><font color="Green" title="E25">A2</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G1</font> <a href="glib_002.html#K1" title="GLIB_002:func.1">.reachableFrom</a> <font color="Maroon" title="c4">v1</font>
 <b>by </b><i><a class="ref" href="glib_002.html#D8" target="_self" title="GLIB_002:def.8">Def8</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c5">v2</font> = <font color="Maroon" title="c4">v1</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="glib_002.html#E1:40"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="glib_000.html#D36" title="GLIB_000:def.36">GLIB_000:def 36</a></i>;<br/><a NAME="E5:40_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G2</font> <a href="glib_002.html#K1" title="GLIB_002:func.1">.reachableFrom</a> <font color="Maroon" title="c5">v2</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E1:40"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="glib_002.html#E3:40_1_1"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="glib_002.html#E21"><i><font color="Green" title="E20">Lm9</font></i></a></i>;<br/><b>hence </b><a NAME="E6:40_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G2</font> <a href="glib_002.html#K3" title="GLIB_002:func.3">.componentSet()</a> 
 <b>by </b><i><a class="ref" href="glib_002.html#D8" target="_self" title="GLIB_002:def.8">Def8</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:40_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G2</font> <a href="glib_002.html#K3" title="GLIB_002:func.3">.componentSet()</a> 
 ;<br/><b>then consider </b><font color="Maroon" title="c4">v2</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font><b> such that </b><br/><a NAME="E4:40_1"/><i><font color="Green" title="E25">A3</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G2</font> <a href="glib_002.html#K1" title="GLIB_002:func.1">.reachableFrom</a> <font color="Maroon" title="c4">v2</font>
 <b>by </b><i><a class="ref" href="glib_002.html#D8" target="_self" title="GLIB_002:def.8">Def8</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c5">v1</font> = <font color="Maroon" title="c4">v2</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font> <b>by </b><i><a class="txt" href="glib_002.html#E1:40"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="glib_000.html#D36" title="GLIB_000:def.36">GLIB_000:def 36</a></i>;<br/><a NAME="E6:40_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G1</font> <a href="glib_002.html#K1" title="GLIB_002:func.1">.reachableFrom</a> <font color="Maroon" title="c5">v1</font>
 <b>by </b><i><a class="txt" href="glib_002.html#E1:40"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="glib_002.html#E4:40_1"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="glib_002.html#E21"><i><font color="Green" title="E20">Lm9</font></i></a></i>;<br/><b>hence </b><a NAME="E7:40_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G1</font> <a href="glib_002.html#K3" title="GLIB_002:func.3">.componentSet()</a> 
 <b>by </b><i><a class="ref" href="glib_002.html#D8" target="_self" title="GLIB_002:def.8">Def8</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:40"/>
<font color="Maroon" title="c1">G1</font> <a href="glib_002.html#K3" title="GLIB_002:func.3">.componentSet()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G2</font> <a href="glib_002.html#K3" title="GLIB_002:func.3">.componentSet()</a> 
 <b>by </b><i><a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></i>;<br/>


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