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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">V</font> being   <a href="subset_1.html#V1" title="SUBSET_1:attr.1">proper</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G1</font></span>)</span><br/>  for <font color="Olive" title="b2">G2</font> being   <a href="glib_000.html#NM7" title="GLIB_000:NM.7">removeVertices</a> of <font color="Maroon" title="c1">G1</font>,<font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b3">G3</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="b4">G4</font> being   <a href="glib_000.html#NM7" title="GLIB_000:NM.7">removeVertices</a> of <font color="Olive" title="b3">G3</font>,<font color="Olive" title="b1">V</font> holds  <font color="Olive" title="b4">G4</font> is    <a href="glib_012.html#M3" title="GLIB_012:mode.3">LGraphComplement</a> of <font color="Olive" title="b2">G2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be   <a href="subset_1.html#V1" title="SUBSET_1:attr.1">proper</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G1</font></span>)</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">  for <font color="Olive" title="b1">G2</font> being   <a href="glib_000.html#NM7" title="GLIB_000:NM.7">removeVertices</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">V</font><br/>  for <font color="Olive" title="b2">G3</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="b3">G4</font> being   <a href="glib_000.html#NM7" title="GLIB_000:NM.7">removeVertices</a> of <font color="Olive" title="b2">G3</font>,<font color="Maroon" title="c2">V</font> holds  <font color="Olive" title="b3">G4</font> is    <a href="glib_012.html#M3" title="GLIB_012:mode.3">LGraphComplement</a> of <font color="Olive" title="b1">G2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">G2</font> be   <a href="glib_000.html#NM7" title="GLIB_000:NM.7">removeVertices</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">V</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">G3</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">G4</font> being   <a href="glib_000.html#NM7" title="GLIB_000:NM.7">removeVertices</a> of <font color="Olive" title="b1">G3</font>,<font color="Maroon" title="c2">V</font> holds  <font color="Olive" title="b2">G4</font> is    <a href="glib_012.html#M3" title="GLIB_012:mode.3">LGraphComplement</a> of <font color="Maroon" title="c3">G2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">G3</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">G4</font> being   <a href="glib_000.html#NM7" title="GLIB_000:NM.7">removeVertices</a> of <font color="Maroon" title="c4">G3</font>,<font color="Maroon" title="c2">V</font> holds  <font color="Olive" title="b1">G4</font> is    <a href="glib_012.html#M3" title="GLIB_012:mode.3">LGraphComplement</a> of <font color="Maroon" title="c3">G2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">G4</font> be   <a href="glib_000.html#NM7" title="GLIB_000:NM.7">removeVertices</a> of <font color="Maroon" title="c4">G3</font>,<font color="Maroon" title="c2">V</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="c5">G4</font> is    <a href="glib_012.html#M3" title="GLIB_012:mode.3">LGraphComplement</a> of <font color="Maroon" title="c3">G2</font></span><br/>









<a NAME="E1:116"/>
( <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c2">V</font> is   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G1</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c2">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c4">G3</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c2">V</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_012.html#D7" target="_self" onmouseover="rs('glib_012/D7')" onmouseout="rh()">Def7</a>, <a class="ref" href="xboole_1.html#T105" onmouseover="rs('xboole_1/T105')" onmouseout="rh()">XBOOLE_1:105</a>, <a class="ref" href="glibpre0.html#T6" onmouseover="rs('glibpre0/T6')" onmouseout="rh()">GLIBPRE0:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:116"/>
<font color="Maroon" title="c5">G4</font> is    <a href="glib_012.html#M3" title="GLIB_012:mode.3">LGraphComplement</a> of <font color="Maroon" title="c3">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_012.html#T69" target="_self" onmouseover="rs('glib_012/T69')" onmouseout="rh()">Th69</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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