<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">G</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   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">G</font></span>)</span><br/>  for <font color="Olive" title="b2">H</font> being    <a href="glib_000.html#M2" title="GLIB_000:mode.2">inducedSubgraph</a> of <font color="Maroon" title="c1">G</font>,<font color="Olive" title="b1">V</font>, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds  <font color="Olive" title="b2">H</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a>  <a href="glenum00.html#K2" title="GLENUM00:func.2">createGraph</a> <font color="Olive" title="b1">V</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be   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">G</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">H</font> being    <a href="glib_000.html#M2" title="GLIB_000:mode.2">inducedSubgraph</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">V</font>, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds  <font color="Olive" title="b1">H</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a>  <a href="glenum00.html#K2" title="GLENUM00:func.2">createGraph</a> <font color="Maroon" title="c2">V</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">H</font> be    <a href="glib_000.html#M2" title="GLIB_000:mode.2">inducedSubgraph</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">V</font>, <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"> <font color="Maroon" title="c3">H</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a>  <a href="glenum00.html#K2" title="GLENUM00:func.2">createGraph</a> <font color="Maroon" title="c2">V</font></span><br/>





<a NAME="E1:9"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.edgesBetween</a> <font color="Maroon" title="c2">V</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T2" onmouseover="rs('xboole_1/T2')" onmouseout="rh()">XBOOLE_1:2</a></span>;<br/>
<a NAME="E2:9"/><span class="kw">then </span>
(  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c3">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <span class="p1">(<span class="default"><a href="glenum00.html#K2" title="GLENUM00:func.2">createGraph</a> <font color="Maroon" title="c2">V</font></span>)</span> &amp;  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c3">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <span class="p1">(<span class="default"><a href="glenum00.html#K2" title="GLENUM00:func.2">createGraph</a> <font color="Maroon" title="c2">V</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D37" onmouseover="rs('glib_000/D37')" onmouseout="rh()">GLIB_000:def 37</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:9"/>
<font color="Maroon" title="c3">H</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a>  <a href="glenum00.html#K2" title="GLENUM00:func.2">createGraph</a> <font color="Maroon" title="c2">V</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T86" onmouseover="rs('glib_000/T86')" onmouseout="rh()">GLIB_000:86</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>
