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<span class="kw">let </span><font color="Maroon" title="c1">G1</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</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"> ( <font color="Maroon" title="c1">G1</font> is  <a href="glib_012.html#V4" title="GLIB_012:attr.4">self-Lcomplementary</a>  implies (  not <font color="Maroon" title="c1">G1</font> is  <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a>  &amp;  not <font color="Maroon" title="c1">G1</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  &amp; <font color="Maroon" title="c1">G1</font> is  <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a>  &amp; <font color="Maroon" title="c1">G1</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a>  ) )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">G2</font> =  the    <a href="glib_012.html#M3" title="GLIB_012:mode.3">LGraphComplement</a> of <font color="Maroon" title="c1">G1</font>;<br/>
<span class="kw">assume </span><a NAME="E1:192_2_1"/>
<font color="Maroon" title="c1">G1</font> is  <a href="glib_012.html#V4" title="GLIB_012:attr.4">self-Lcomplementary</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"> (  not <font color="Maroon" title="c1">G1</font> is  <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a>  &amp;  not <font color="Maroon" title="c1">G1</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  &amp; <font color="Maroon" title="c1">G1</font> is  <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a>  &amp; <font color="Maroon" title="c1">G1</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a>  )</span><br/>

<a NAME="E2:192_2_1"/><span class="kw">then </span>
 the    <a href="glib_012.html#M3" title="GLIB_012:mode.3">LGraphComplement</a> of <font color="Maroon" title="c1">G1</font> is <font color="Maroon" title="c1">G1</font> <a href="glib_010.html#V19" title="GLIB_010:attr.19">-isomorphic</a> 
 
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">F</font> being    <a href="glib_010.html#M1" title="GLIB_010:mode.1">PGraphMapping</a> of <font color="Maroon" title="c1">G1</font>, the    <a href="glib_012.html#M3" title="GLIB_012:mode.3">LGraphComplement</a> of <font color="Maroon" title="c1">G1</font><span class="kw"> such that </span><br/><a NAME="E4:192_2_1"/><span class="lab"><font color="Green" title="E89">A2</font></span>: 
<font color="Maroon" title="c3">F</font> is  <a href="glib_010.html#V17" title="GLIB_010:attr.17">isomorphism</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_010.html#D23" onmouseover="rs('glib_010/D23')" onmouseout="rh()">GLIB_010:def 23</a></span>;<br/>
<span class="kw">thus </span><a NAME="E5:192_2_1"/>
(  not <font color="Maroon" title="c1">G1</font> is  <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a>  &amp;  not <font color="Maroon" title="c1">G1</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  &amp; <font color="Maroon" title="c1">G1</font> is  <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a>  &amp; <font color="Maroon" title="c1">G1</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:192_2_1"><span class="lab"><font color="Green" title="E89">A2</font></span></a>, <a class="ref" href="glib_010.html#T89" onmouseover="rs('glib_010/T89')" onmouseout="rh()">GLIB_010:89</a>, <a class="ref" href="glib_010.html#T140" onmouseover="rs('glib_010/T140')" onmouseout="rh()">GLIB_010:140</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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