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<span class="kw">let </span><font color="Maroon" title="c3">G1</font> be    <a href="glib_006.html#M2" title="GLIB_006:mode.2">addVertices</a> of <font color="Maroon" title="c1">G</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">  not <font color="Maroon" title="c3">G1</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a> </span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:17_1_1_1"/>
( <font color="Maroon" title="c2">V</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</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="c1">G</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Maroon" title="c2">V</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</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="c1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:17_1_1_1_1"/>
<font color="Maroon" title="c2">V</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</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="c1">G</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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="c3">G1</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a> </span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:17_1_1_1_1"/>
 not <font color="Maroon" title="c3">G1</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_012.html#T11" target="_self" onmouseover="rs('glib_012/T11')" onmouseout="rh()">Th11</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:17_1_1_1_2"/>
<font color="Maroon" title="c2">V</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</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="c1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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="c3">G1</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a> </span><br/><div class="add"><a NAME="E2:17_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">G</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c3">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_006.html#T78" onmouseover="rs('glib_006/T78')" onmouseout="rh()">GLIB_006:78</a>, <a class="ref" href="xboole_1.html#T37" onmouseover="rs('xboole_1/T37')" onmouseout="rh()">XBOOLE_1:37</a></span>;<br/><span class="kw">hence </span><a NAME="E3:17_1_1_1_2"/>
 not <font color="Maroon" title="c3">G1</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_012.html#T4" target="_self" onmouseover="rs('glib_012/T4')" onmouseout="rh()">Th4</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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