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<b>set </b><font color="Maroon" title="c2">G2</font> = <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K14" title="GLIB_000:func.14">.strict</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a>  implies <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">G</font> )</span><br/><b>assume </b><a NAME="E1:14_1_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">G</font></span><br/><a NAME="E2:14_1_1_1"/><b>then </b>
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K1" title="GLIB_000:func.1">VertexSelector</a>  or <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K2" title="GLIB_000:func.2">EdgeSelector</a>  or <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K3" title="GLIB_000:func.3">SourceSelector</a>  or <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K4" title="GLIB_000:func.4">TargetSelector</a>  )
 <b>by </b><i><a class="ref" href="enumset1.html#D2" title="ENUMSET1:def.2">ENUMSET1:def 2</a></i>;<br/><b>hence </b><a NAME="E3:14_1_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D11" target="_self" title="GLIB_000:def.11">Def11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E2:14_1_1"/><b>then </b><i><font color="Green" title="E4">A1</font></i>: 
 <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<i><font color="Green" title="E5">A2</font></i>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K14" title="GLIB_000:func.14">.strict</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a> </span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a> 
<b>by </b><i><a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></i>
<br/>.= 
 <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a> 
<b>by </b><i><a class="txt" href="glib_000.html#E2:14_1_1"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></i>
;<br/>
<a NAME="E4:14_1_1"/><i><font color="Green" title="E6">A3</font></i>: 
(  <a href="glib_000.html#K1" title="GLIB_000:func.1">VertexSelector</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a>  &amp;  <a href="glib_000.html#K2" title="GLIB_000:func.2">EdgeSelector</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a>  &amp;  <a href="glib_000.html#K3" title="GLIB_000:func.3">SourceSelector</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a>  &amp;  <a href="glib_000.html#K4" title="GLIB_000:func.4">TargetSelector</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a>  )
 
<b>by </b><i><a class="ref" href="enumset1.html#D2" title="ENUMSET1:def.2">ENUMSET1:def 2</a></i>;<br/>
<a NAME="E5:14_1_1"/><b>then </b><i><font color="Green" title="E7">A4</font></i>: 
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K14" title="GLIB_000:func.14">.strict</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a> </span>)</span> <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">G</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>;<br/>
<a NAME="E6:14_1_1"/><i><font color="Green" title="E8">A5</font></i>: 
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K14" title="GLIB_000:func.14">.strict</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="txt" href="glib_000.html#E4:14_1_1"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>;<br/>
<a NAME="E7:14_1_1"/><i><font color="Green" title="E9">A6</font></i>: 
 <a href="glib_000.html#K8" title="GLIB_000:func.8">the_Source_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K14" title="GLIB_000:func.14">.strict</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="txt" href="glib_000.html#E4:14_1_1"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>;<br/>
<a NAME="E8:14_1_1"/>
 <a href="glib_000.html#K9" title="GLIB_000:func.9">the_Target_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K14" title="GLIB_000:func.14">.strict</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="txt" href="glib_000.html#E4:14_1_1"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>;<br/>
<b>hence </b><a NAME="E9:14_1_1"/>
<font color="Maroon" title="c1">G</font> <a href="glib_000.html#K14" title="GLIB_000:func.14">.strict</a> <a href="glib_000.html#K5" title="GLIB_000:func.5">_GraphSelectors</a>  is <a href="glib_000.html#V1" title="GLIB_000:attr.1">[Graph-like]</a>
 <b>by </b><i><a class="txt" href="glib_000.html#E3:14_1_1"><i><font color="Green" title="E5">A2</font></i></a>, <a class="txt" href="glib_000.html#E5:14_1_1"><i><font color="Green" title="E7">A4</font></i></a>, <a class="txt" href="glib_000.html#E6:14_1_1"><i><font color="Green" title="E8">A5</font></i></a>, <a class="txt" href="glib_000.html#E7:14_1_1"><i><font color="Green" title="E9">A6</font></i></a>, <a class="txt" href="glib_000.html#E15"><i><font color="Green" title="E3">Lm1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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