<?xml version="1.0"?>
<div class="add">

<span class="kw">set </span><font color="Maroon" title="c1">E</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c2">V</font> = <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">S</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <span class="kw">by</span> <span class="lab"><a class="ref" href="relset_1.html#T25" title="RELSET_1:th.25">RELSET_1:25</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">G1</font> =  <a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c3">S</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">WL</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <span class="p2">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c3">S</font></span>)</span></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">G2</font> = <span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c3">S</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c5">WL</font>;<br/>
<span class="kw">take </span>
<span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c3">S</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c5">WL</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c3">S</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c5">WL</font> is  <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a>  &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c3">S</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c5">WL</font> is  <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a>  &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c3">S</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c5">WL</font> is  <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a>  &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c3">S</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c5">WL</font> is  <a href="glib_005.html#V1" title="GLIB_005:attr.1">natural-weighted</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E3:7_1_1"/>
( <span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c3">S</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c5">WL</font> is  <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a>  &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c3">S</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c5">WL</font> is  <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a>  &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c3">S</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c5">WL</font> is  <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c3">S</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c5">WL</font> is  <a href="glib_005.html#V1" title="GLIB_005:attr.1">natural-weighted</a> </span><br/>

<a NAME="E4:7_1_1"/>
 <a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c3">S</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c5">WL</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">WL</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T11" title="GLIB_000:th.11">GLIB_000:11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:7_1_1"/>
<span class="p1">(<span class="default"><a href="glib_000.html#K12" title="GLIB_000:func.12">createGraph</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c3">S</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c5">WL</font> is  <a href="glib_005.html#V1" title="GLIB_005:attr.1">natural-weighted</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_005.html#D1" target="_self" title="GLIB_005:def.1">Def1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
