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<span class="kw">let </span><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font>, <font color="Maroon" title="c3">G3</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">  for <font color="Olive" title="b1">G4</font> being    <a href="glib_012.html#M5" title="GLIB_012:mode.5">GraphComplement</a> of <font color="Maroon" title="c1">G1</font>  st <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> &amp; <font color="Maroon" title="c3">G3</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Olive" title="b1">G4</font> holds <br/><font color="Maroon" title="c3">G3</font> is    <a href="glib_012.html#M5" title="GLIB_012:mode.5">GraphComplement</a> of <font color="Maroon" title="c2">G2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">G4</font> be    <a href="glib_012.html#M5" title="GLIB_012:mode.5">GraphComplement</a> of <font color="Maroon" title="c1">G1</font>; <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> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">G2</font> &amp; <font color="Maroon" title="c3">G3</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c4">G4</font> implies <font color="Maroon" title="c3">G3</font> is    <a href="glib_012.html#M5" title="GLIB_012:mode.5">GraphComplement</a> of <font color="Maroon" title="c2">G2</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:158"/><span class="lab"><font color="Green" title="E74">A1</font></span>: 
( <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> &amp; <font color="Maroon" title="c3">G3</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c4">G4</font> )
 ; <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="c3">G3</font> is    <a href="glib_012.html#M5" title="GLIB_012:mode.5">GraphComplement</a> of <font color="Maroon" title="c2">G2</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c5">G9</font> being    <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="E3:158"/><span class="lab"><font color="Green" title="E75">A2</font></span>: 
<font color="Maroon" title="c4">G4</font> is   <a href="glib_009.html#NM1" title="GLIB_009:NM.1">removeLoops</a> of <font color="Maroon" title="c5">G9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_012.html#D9" target="_self" onmouseover="rs('glib_012/D9')" onmouseout="rh()">Def9</a></span>;<br/>
<a NAME="E4:158"/>
( <font color="Maroon" title="c5">G9</font> is    <a href="glib_012.html#M3" title="GLIB_012:mode.3">LGraphComplement</a> of <font color="Maroon" title="c2">G2</font> &amp; <font color="Maroon" title="c3">G3</font> is   <a href="glib_009.html#NM1" title="GLIB_009:NM.1">removeLoops</a> of <font color="Maroon" title="c5">G9</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:158"><span class="lab"><font color="Green" title="E74">A1</font></span></a>, <a class="txt" href="#E3:158"><span class="lab"><font color="Green" title="E75">A2</font></span></a>, <a class="ref" href="glib_012.html#T62" target="_self" onmouseover="rs('glib_012/T62')" onmouseout="rh()">Th62</a>, <a class="ref" href="glib_009.html#T59" onmouseover="rs('glib_009/T59')" onmouseout="rh()">GLIB_009:59</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:158"/>
<font color="Maroon" title="c3">G3</font> is    <a href="glib_012.html#M5" title="GLIB_012:mode.5">GraphComplement</a> of <font color="Maroon" title="c2">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_012.html#D9" target="_self" onmouseover="rs('glib_012/D9')" onmouseout="rh()">Def9</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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