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<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   non  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <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">e</font> being   <a href="glib_008.html#NM1" title="GLIB_008:NM.1">Edge</a> of <font color="Maroon" title="c1">G</font><br/>  for <font color="Olive" title="b2">H</font> being   <a href="glib_009.html#V1" title="GLIB_009:attr.1">plain</a>   <a href="glib_006.html#M2" title="GLIB_006:mode.2">addVertices</a> of  <a href="glenum00.html#K4" title="GLENUM00:func.4">createGraph</a> <font color="Olive" title="b1">e</font>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font> holds  <font color="Olive" title="b2">H</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K8" title="GLENUM00:func.8">.allSpanningSG()</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">e</font> be   <a href="glib_008.html#NM1" title="GLIB_008:NM.1">Edge</a> of <font color="Maroon" title="c1">G</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">H</font> being   <a href="glib_009.html#V1" title="GLIB_009:attr.1">plain</a>   <a href="glib_006.html#M2" title="GLIB_006:mode.2">addVertices</a> of  <a href="glenum00.html#K4" title="GLENUM00:func.4">createGraph</a> <font color="Maroon" title="c2">e</font>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font> holds  <font color="Olive" title="b1">H</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K8" title="GLENUM00:func.8">.allSpanningSG()</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">H</font> be   <a href="glib_009.html#V1" title="GLIB_009:attr.1">plain</a>   <a href="glib_006.html#M2" title="GLIB_006:mode.2">addVertices</a> of  <a href="glenum00.html#K4" title="GLENUM00:func.4">createGraph</a> <font color="Maroon" title="c2">e</font>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</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="c3">H</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K8" title="GLENUM00:func.8">.allSpanningSG()</a> </span><br/>





<span class="lab"><font color="Green" title="E56">A1</font></span>:  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c3">H</font> = 
<span class="p1">(<span class="default"><a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <span class="p2">(<span class="default"><a href="glenum00.html#K4" title="GLENUM00:func.4">createGraph</a> <font color="Maroon" title="c2">e</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_006.html#D10" onmouseover="rs('glib_006/D10')" onmouseout="rh()">GLIB_006:def 10</a></span>
<br/>.= 
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T12" onmouseover="rs('xboole_1/T12')" onmouseout="rh()">XBOOLE_1:12</a></span>
;<br/>
<a NAME="E2:96"/>
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font>
 
;<br/>
<a NAME="E3:96"/><span class="kw">then </span>
<font color="Maroon" title="c3">H</font> is   <a href="glib_000.html#V9" title="GLIB_000:attr.9">spanning</a>   <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c1">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:96"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="ref" href="glenum00.html#T21" target="_self" onmouseover="rs('glenum00/T21')" onmouseout="rh()">Th21</a>, <a class="ref" href="glib_000.html#D33" onmouseover="rs('glib_000/D33')" onmouseout="rh()">GLIB_000:def 33</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:96"/>
<font color="Maroon" title="c3">H</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K8" title="GLENUM00:func.8">.allSpanningSG()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glenum00.html#T60" target="_self" onmouseover="rs('glenum00/T60')" onmouseout="rh()">Th60</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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