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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">H</font> being    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c1">G</font> holds  <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">H</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glenum00.html#K6" title="GLENUM00:func.6">SubgraphRel</a> <font color="Maroon" title="c1">G</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">H</font> be    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</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"> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">H</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glenum00.html#K6" title="GLENUM00:func.6">SubgraphRel</a> <font color="Maroon" title="c1">G</font></span><br/>



<a NAME="E1:57"/><span class="lab"><font color="Green" title="E36">A1</font></span>: 
( <font color="Maroon" title="c2">H</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">H</font> &amp; <font color="Maroon" title="c1">G</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c1">G</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T128" onmouseover="rs('glib_000/T128')" onmouseout="rh()">GLIB_000:128</a></span>;<br/>
<a NAME="E2:57"/><span class="lab"><font color="Green" title="E37">A2</font></span>: 
( <font color="Maroon" title="c2">H</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a> <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>  &amp; <font color="Maroon" title="c1">G</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a> <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#T2" target="_self" onmouseover="rs('glenum00/T2')" onmouseout="rh()">Th2</a>, <a class="ref" href="glenum00.html#T3" target="_self" onmouseover="rs('glenum00/T3')" onmouseout="rh()">Th3</a></span>;<br/>
<a NAME="E3:57"/>
<font color="Maroon" title="c2">H</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a> is    <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="#E1:57"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="glib_000.html#T92" onmouseover="rs('glib_000/T92')" onmouseout="rh()">GLIB_000:92</a></span>;<br/>
<a NAME="E4:57"/><span class="kw">then </span>
<font color="Maroon" title="c2">H</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c1">G</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="glib_000.html#T91" onmouseover="rs('glib_000/T91')" onmouseout="rh()">GLIB_000:91</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:57"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">H</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glenum00.html#K6" title="GLENUM00:func.6">SubgraphRel</a> <font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="ref" href="glenum00.html#D6" target="_self" onmouseover="rs('glenum00/D6')" onmouseout="rh()">Def6</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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