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<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">S</font>, <font color="Olive" title="b3">T</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<font color="Olive" title="b1">V</font> holds   <a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<font color="Olive" title="b1">V</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<font color="Olive" title="b2">S</font>,<font color="Olive" title="b3">T</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a> </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">S</font>, <font color="Olive" title="b2">T</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<font color="Maroon" title="c2">V</font> holds   <a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<font color="Maroon" title="c2">V</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">T</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">S</font>, <font color="Maroon" title="c4">T</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<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">  <a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<font color="Maroon" title="c2">V</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c4">T</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a> </span><br/>





<span class="kw">set </span><font color="Maroon" title="c5">H</font> =  <a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<font color="Maroon" title="c2">V</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c4">T</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c6">H9</font> =  the   <a href="glib_009.html#V1" title="GLIB_009:attr.1">plain</a>   <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> ;<br/>
<a NAME="E1:6"/>
 <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="E2:6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E5">A1</font></span>: 
(  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a>  the   <a href="glib_009.html#V1" title="GLIB_009:attr.1">plain</a>   <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 href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">V</font> &amp;  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a>  the   <a href="glib_009.html#V1" title="GLIB_009:attr.1">plain</a>   <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 href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<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/>
<a NAME="E3:6"/><span class="lab"><font color="Green" title="E6">A2</font></span>: 
(  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a>  the   <a href="glib_009.html#V1" title="GLIB_009:attr.1">plain</a>   <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 href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a>  the   <a href="glib_009.html#V1" title="GLIB_009:attr.1">plain</a>   <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 href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E5">A1</font></span></a></span>;<br/>
<a NAME="E4:6"/>
(  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<font color="Maroon" title="c2">V</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c4">T</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">V</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<font color="Maroon" title="c2">V</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c4">T</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>  &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<font color="Maroon" title="c2">V</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c4">T</font>)</span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c3">S</font> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<font color="Maroon" title="c2">V</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c4">T</font>)</span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c4">T</font> )
 
;<br/>
<a NAME="E5:6"/><span class="kw">then </span>
 <a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<font color="Maroon" title="c2">V</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c4">T</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the   <a href="glib_009.html#V1" title="GLIB_009:attr.1">plain</a>   <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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="txt" href="#E3:6"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="ref" href="glib_000.html#D34" onmouseover="rs('glib_000/D34')" onmouseout="rh()">GLIB_000:def 34</a>, <a class="ref" href="glib_009.html#T44" onmouseover="rs('glib_009/T44')" onmouseout="rh()">GLIB_009:44</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:6"/>
 <a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> (<font color="Maroon" title="c2">V</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c4">T</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glenum00.html#T1" target="_self" onmouseover="rs('glenum00/T1')" onmouseout="rh()">Th1</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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