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<span class="kw">let </span><font color="Maroon" title="c1">G2</font> be   <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</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">G1</font> being    <a href="glib_006.html#M1" title="GLIB_006:mode.1">Supergraph</a> of <font color="Maroon" title="c1">G2</font>  st  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Olive" title="b1">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G2</font> holds <br/><font color="Olive" title="b1">G1</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">G1</font> be    <a href="glib_006.html#M1" title="GLIB_006:mode.1">Supergraph</a> of <font color="Maroon" title="c1">G2</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#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c2">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G2</font> implies <font color="Maroon" title="c2">G1</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:9"/><span class="lab"><font color="Green" title="E6">A1</font></span>: 
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c2">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G2</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="c2">G1</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">v</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G1</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="glib_012.html#D1" target="_self" onmouseover="rs('glib_012/D1')" onmouseout="rh()">GLIB_012:def 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">  ex <font color="Olive" title="b1">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <font color="Olive" title="b1">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c2">G1</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c4">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:9"/><span class="lab"><font color="Green" title="E7">A2</font></span>: 
<font color="Maroon" title="c4">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c1">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:9"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="glib_012.html#D1" target="_self" onmouseover="rs('glib_012/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">e</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="c4">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c2">G1</font></span><br/>

<span class="kw">thus </span><a NAME="E4:9"/>
<font color="Maroon" title="c4">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c2">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:9"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="ref" href="glib_006.html#T70" onmouseover="rs('glib_006/T70')" onmouseout="rh()">GLIB_006:70</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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