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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">H</font> being   <a href="glib_000.html#NM5" title="GLIB_000:NM.5">inducedSubgraph</a> of <font color="Maroon" title="c1">G</font>,<font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b3">E</font> being    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Maroon" title="c1">G</font> holds  <font color="Olive" title="b3">E</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.edgesBetween</a> <font color="Olive" title="b1">V</font></span>)</span> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Olive" title="b2">H</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#NM5" title="GLIB_000:NM.5">inducedSubgraph</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">V</font><br/>  for <font color="Olive" title="b2">E</font> being    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Maroon" title="c1">G</font> holds  <font color="Olive" title="b2">E</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><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>)</span> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Olive" title="b1">H</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">H</font> be   <a href="glib_000.html#NM5" title="GLIB_000:NM.5">inducedSubgraph</a> of <font color="Maroon" title="c1">G</font>,<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">  for <font color="Olive" title="b1">E</font> being    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Maroon" title="c1">G</font> holds  <font color="Olive" title="b1">E</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><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>)</span> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Maroon" title="c3">H</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">E</font> be    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</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"> <font color="Maroon" title="c4">E</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><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>)</span> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Maroon" title="c3">H</font></span><br/>







<a NAME="E1:81"/>
<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> <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> <font color="Maroon" title="c3">H</font>
 
<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">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">E9</font> = <font color="Maroon" title="c4">E</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><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>)</span> as   <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#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c3">H</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T17" onmouseover="rs('xboole_1/T17')" onmouseout="rh()">XBOOLE_1:17</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="81_1"><span class="kw">now </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">v</font>, <font color="Olive" title="b2">w</font>, <font color="Olive" title="b3">e0</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b3">e0</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">w</font>,<font color="Maroon" title="c3">H</font> holds <br/> ex <font color="Olive" title="b4">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b4">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">w</font>,<font color="Maroon" title="c3">H</font> &amp; <font color="Olive" title="b4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">E9</font> &amp; (  for <font color="Olive" title="b5">e9</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b5">e9</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">w</font>,<font color="Maroon" title="c3">H</font> &amp; <font color="Olive" title="b5">e9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">E9</font> holds <br/><font color="Olive" title="b5">e9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">e</font> ) )</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">v</font>, <font color="Maroon" title="c7">w</font>, <font color="Maroon" title="c8">e0</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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="c8">e0</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c3">H</font> implies  ex <font color="Olive" title="b1">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c3">H</font> &amp; <font color="Olive" title="b1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">E9</font> &amp; (  for <font color="Olive" title="b2">e9</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b2">e9</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c3">H</font> &amp; <font color="Olive" title="b2">e9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">E9</font> holds <br/><font color="Olive" title="b2">e9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">e</font> ) ) )</span><br/><a NAME="E1:81_1"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
( <font color="Maroon" title="c6">v</font> is    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  &amp; <font color="Maroon" title="c7">w</font> is    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#T1" onmouseover="rs('tarski/T1')" onmouseout="rh()">TARSKI:1</a></span>;<br/><span class="kw">assume </span><a NAME="E2:81_1"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
<font color="Maroon" title="c8">e0</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c3">H</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">  ex <font color="Olive" title="b1">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c3">H</font> &amp; <font color="Olive" title="b1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">E9</font> &amp; (  for <font color="Olive" title="b2">e9</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b2">e9</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c3">H</font> &amp; <font color="Olive" title="b2">e9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">E9</font> holds <br/><font color="Olive" title="b2">e9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">e</font> ) )</span><br/><a NAME="E3:81_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">e0</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:81_1"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="glib_000.html#T72" onmouseover="rs('glib_000/T72')" onmouseout="rh()">GLIB_000:72</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E5:81_1"/><span class="lab"><font color="Green" title="E20">A3</font></span>: 
( <font color="Maroon" title="c9">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c1">G</font> &amp; <font color="Maroon" title="c9">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">E</font> )
 <span class="kw">and </span><br/><a NAME="E6:81_1"/><span class="lab"><font color="Green" title="E21">A4</font></span>: 
 for <font color="Olive" title="b1">e9</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">e9</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c1">G</font> &amp; <font color="Olive" title="b1">e9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">E</font> holds <br/><font color="Olive" title="b1">e9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">e</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_009.html#D5" onmouseover="rs('glib_009/D5')" onmouseout="rh()">GLIB_009:def 5</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c10">e</font> = <font color="Maroon" title="c9">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="c10">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c3">H</font> &amp; <font color="Maroon" title="c10">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">E9</font> &amp; (  for <font color="Olive" title="b1">e9</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">e9</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c3">H</font> &amp; <font color="Olive" title="b1">e9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">E9</font> holds <br/><font color="Olive" title="b1">e9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">e</font> ) )</span><br/><a NAME="E7:81_1"/>
( <font color="Maroon" title="c6">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c3">H</font> &amp; <font color="Maroon" title="c7">w</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c3">H</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:81_1"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="glib_000.html#T13" onmouseover="rs('glib_000/T13')" onmouseout="rh()">GLIB_000:13</a></span>;<br/><a NAME="E8:81_1"/><span class="kw">then </span>
( <font color="Maroon" title="c6">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">V</font> &amp; <font color="Maroon" title="c7">w</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">V</font> )
 <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="E9:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A5</font></span>: 
<font color="Maroon" title="c10">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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="txt" href="#E5:81_1"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="glib_000.html#T32" onmouseover="rs('glib_000/T32')" onmouseout="rh()">GLIB_000:32</a></span>;<br/><a NAME="E10:81_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c3">H</font>
 <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="E11:81_1"/>
<font color="Maroon" title="c10">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c3">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:81_1"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E5:81_1"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="glib_000.html#T73" onmouseover="rs('glib_000/T73')" onmouseout="rh()">GLIB_000:73</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"> ( <font color="Maroon" title="c10">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">E9</font> &amp; (  for <font color="Olive" title="b1">e9</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">e9</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c3">H</font> &amp; <font color="Olive" title="b1">e9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">E9</font> holds <br/><font color="Olive" title="b1">e9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">e</font> ) )</span><br/><span class="kw">thus </span><a NAME="E12:81_1"/>
<font color="Maroon" title="c10">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">E9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:81_1"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E9:81_1"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="xboole_0.html#D4" onmouseover="rs('xboole_0/D4')" onmouseout="rh()">XBOOLE_0:def 4</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">  for <font color="Olive" title="b1">e9</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">e9</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c3">H</font> &amp; <font color="Olive" title="b1">e9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">E9</font> holds <br/><font color="Olive" title="b1">e9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">e</font></span><br/><span class="kw">let </span><font color="Maroon" title="c11">e9</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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="c11">e9</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c3">H</font> &amp; <font color="Maroon" title="c11">e9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">E9</font> implies <font color="Maroon" title="c11">e9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">e</font> )</span><br/><span class="kw">assume </span><a NAME="E13:81_1"/>
( <font color="Maroon" title="c11">e9</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c3">H</font> &amp; <font color="Maroon" title="c11">e9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">E9</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="c11">e9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">e</font></span><br/><a NAME="E14:81_1"/><span class="kw">then </span>
( <font color="Maroon" title="c11">e9</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">w</font>,<font color="Maroon" title="c1">G</font> &amp; <font color="Maroon" title="c11">e9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">E</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:81_1"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="glib_000.html#T72" onmouseover="rs('glib_000/T72')" onmouseout="rh()">GLIB_000:72</a>, <a class="ref" href="xboole_0.html#D4" onmouseover="rs('xboole_0/D4')" onmouseout="rh()">XBOOLE_0:def 4</a></span>;<br/><span class="kw">hence </span><a NAME="E15:81_1"/>
<font color="Maroon" title="c11">e9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:81_1"><span class="lab"><font color="Green" title="E21">A4</font></span></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><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:81"/>
<font color="Maroon" title="c4">E</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><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>)</span> is    <a href="glib_009.html#M1" title="GLIB_009:mode.1">RepEdgeSelection</a> of <font color="Maroon" title="c3">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_009.html#D5" onmouseover="rs('glib_009/D5')" onmouseout="rh()">GLIB_009:def 5</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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