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<span class="kw">assume </span><a NAME="E1:12_1_1"/>
 not  <a href="glib_006.html#K6" title="GLIB_006:func.6">Endvertices</a> <font color="Maroon" title="c1">G</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:12_1_1"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_006.html#K6" title="GLIB_006:func.6">Endvertices</a> <font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D1" onmouseover="rs('xboole_0/D1')" onmouseout="rh()">XBOOLE_0:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">x</font> = <font color="Maroon" title="c2">x</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:12_1_1"><span class="lab"><font color="Green" title="E11">A1</font></span></a></span>;<br/>
<span class="kw">thus </span><a NAME="E5:12_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:12_1_1"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="glib_006.html#T56" onmouseover="rs('glib_006/T56')" onmouseout="rh()">GLIB_006:56</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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