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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">  for <font color="Olive" title="b1">G2</font> being    <a href="glib_012.html#M3" title="GLIB_012:mode.3">LGraphComplement</a> of <font color="Maroon" title="c1">G1</font><br/>  for <font color="Olive" title="b2">e1</font>, <font color="Olive" title="b3">e2</font>, <font color="Olive" title="b4">v</font>, <font color="Olive" title="b5">w</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b2">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b4">v</font>,<font color="Olive" title="b5">w</font>,<font color="Maroon" title="c1">G1</font> holds <br/> not <font color="Olive" title="b3">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b4">v</font>,<font color="Olive" title="b5">w</font>,<font color="Olive" title="b1">G2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">G2</font> be    <a href="glib_012.html#M3" title="GLIB_012:mode.3">LGraphComplement</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">  for <font color="Olive" title="b1">e1</font>, <font color="Olive" title="b2">e2</font>, <font color="Olive" title="b3">v</font>, <font color="Olive" title="b4">w</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">w</font>,<font color="Maroon" title="c1">G1</font> holds <br/> not <font color="Olive" title="b2">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">w</font>,<font color="Maroon" title="c2">G2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">e1</font>, <font color="Maroon" title="c4">e2</font>, <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c6">w</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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="c3">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c1">G1</font> implies  not <font color="Maroon" title="c4">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c2">G2</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:110"/><span class="lab"><font color="Green" title="E49">A1</font></span>: 
<font color="Maroon" title="c3">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font>,<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">  not <font color="Maroon" title="c4">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c2">G2</font></span><br/>

<a NAME="E2:110"/><span class="kw">then </span>
( <font color="Maroon" title="c5">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G1</font> &amp; <font color="Maroon" title="c6">w</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T13" onmouseover="rs('glib_000/T13')" onmouseout="rh()">GLIB_000:13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:110"/>
 not <font color="Maroon" title="c4">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c2">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:110"><span class="lab"><font color="Green" title="E49">A1</font></span></a>, <a class="ref" href="glib_012.html#D7" target="_self" onmouseover="rs('glib_012/D7')" onmouseout="rh()">Def7</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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