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

<span class="kw">consider </span><font color="Maroon" title="c1">G</font> being   <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a>   <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a>   <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a>   <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a>   <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a>   <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a>   <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a>   <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a>   <a href="glib_003.html#V8" title="GLIB_003:attr.8">nonnegative-weighted</a>   <a href="glib_003.html#V11" title="GLIB_003:attr.11">real-WEV</a>  <a href="glib_003.html#NM7" title="GLIB_003:NM.7">WEVGraph</a>;<br/>
<span class="kw">set </span><font color="Maroon" title="c2">F</font> = <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c1">G</font>;<br/>
<a NAME="E2:150_1_1"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">F</font> = <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c1">G</font> as   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="150_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">x</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> is   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a></span><br/><a NAME="E1:150_1_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></span>;<br/><a NAME="E2:150_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:150_1_1"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></span>;<br/><a NAME="E3:150_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">G</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T14" title="FUNCOP_1:th.14">FUNCOP_1:14</a></span>;<br/><span class="kw">hence </span><a NAME="E4:150_1_1_1"/>
<font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> is   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</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><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">F</font> = <font color="Maroon" title="c3">F</font> as   <a href="glib_000.html#NM11" title="GLIB_000:NM.11">GraphSeq</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D55" title="GLIB_000:def.55">GLIB_000:def 55</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="150_1_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">x</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c5">x</font> is  <a href="glib_003.html#V1" title="GLIB_003:attr.1">[Weighted]</a>  &amp; <font color="Maroon" title="c4">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c5">x</font> is  <a href="glib_003.html#V2" title="GLIB_003:attr.2">[ELabeled]</a>  &amp; <font color="Maroon" title="c4">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c5">x</font> is  <a href="glib_003.html#V3" title="GLIB_003:attr.3">[VLabeled]</a>  )</span><br/><a NAME="E1:150_1_1_2"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></span>;<br/><a NAME="E2:150_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:150_1_1"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></span>;<br/><a NAME="E3:150_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">G</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T14" title="FUNCOP_1:th.14">FUNCOP_1:14</a></span>;<br/><span class="kw">hence </span><a NAME="E4:150_1_1_2"/>
( <font color="Maroon" title="c4">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c5">x</font> is  <a href="glib_003.html#V1" title="GLIB_003:attr.1">[Weighted]</a>  &amp; <font color="Maroon" title="c4">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c5">x</font> is  <a href="glib_003.html#V2" title="GLIB_003:attr.2">[ELabeled]</a>  &amp; <font color="Maroon" title="c4">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c5">x</font> is  <a href="glib_003.html#V3" title="GLIB_003:attr.3">[VLabeled]</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</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><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">F</font> = <font color="Maroon" title="c4">F</font> as   <a href="glib_003.html#V12" title="GLIB_003:attr.12">[Weighted]</a>   <a href="glib_003.html#V13" title="GLIB_003:attr.13">[ELabeled]</a>   <a href="glib_003.html#V14" title="GLIB_003:attr.14">[VLabeled]</a>  <a href="glib_000.html#NM11" title="GLIB_000:NM.11">GraphSeq</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_003.html#D24" target="_self" title="GLIB_003:def.24">Def24</a>, <a class="ref" href="glib_003.html#D25" target="_self" title="GLIB_003:def.25">Def25</a>, <a class="ref" href="glib_003.html#D26" target="_self" title="GLIB_003:def.26">Def26</a></span>;<br/>
<a NAME="E8:150_1_1"/>
<font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:150_1_1"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></span>;<br/>
<a NAME="E9:150_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">G</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T14" title="FUNCOP_1:th.14">FUNCOP_1:14</a></span>;<br/>
<a NAME="E10:150_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A2</font></span>: 
<font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c5">F</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">F</font> is  <a href="glib_000.html#V13" title="GLIB_000:attr.13">halting</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_000.html#V14" title="GLIB_000:attr.14">finite</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_000.html#V15" title="GLIB_000:attr.15">loopless</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_000.html#V16" title="GLIB_000:attr.16">trivial</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_000.html#V18" title="GLIB_000:attr.18">non-multi</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_000.html#V20" title="GLIB_000:attr.20">simple</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_003.html#V19" title="GLIB_003:attr.19">real-WEV</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_003.html#V16" title="GLIB_003:attr.16">nonnegative-weighted</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_002.html#V8" title="GLIB_002:attr.8">Tree-like</a>  )</span><br/>

<a NAME="E11:150_1_1"/>
<font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:150_1_1"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></span>;<br/>
<a NAME="E12:150_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">G</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T14" title="FUNCOP_1:th.14">FUNCOP_1:14</a></span>;<br/>
<a NAME="E13:150_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:150_1_1"/>
<font color="Maroon" title="c5">F</font> is  <a href="glib_000.html#V13" title="GLIB_000:attr.13">halting</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:150_1_1"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="ref" href="glib_000.html#D56" title="GLIB_000:def.56">GLIB_000:def 56</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">F</font> is  <a href="glib_000.html#V14" title="GLIB_000:attr.14">finite</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_000.html#V15" title="GLIB_000:attr.15">loopless</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_000.html#V16" title="GLIB_000:attr.16">trivial</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_000.html#V18" title="GLIB_000:attr.18">non-multi</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_000.html#V20" title="GLIB_000:attr.20">simple</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_003.html#V19" title="GLIB_003:attr.19">real-WEV</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_003.html#V16" title="GLIB_003:attr.16">nonnegative-weighted</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_002.html#V8" title="GLIB_002:attr.8">Tree-like</a>  )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="150_1_1_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">x</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c6">x</font> is  <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a>  &amp; <font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c6">x</font> is  <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a>  &amp; <font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c6">x</font> is  <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a>  &amp; <font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c6">x</font> is  <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a>  &amp; <font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c6">x</font> is  <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a>  &amp; <font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c6">x</font> is  <a href="glib_003.html#V11" title="GLIB_003:attr.11">real-WEV</a>  &amp; <font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c6">x</font> is  <a href="glib_003.html#V8" title="GLIB_003:attr.8">nonnegative-weighted</a>  &amp; <font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c6">x</font> is  <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a>  )</span><br/><a NAME="E1:150_1_1_3"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></span>;<br/><a NAME="E2:150_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:150_1_1"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></span>;<br/><a NAME="E3:150_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">G</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T14" title="FUNCOP_1:th.14">FUNCOP_1:14</a></span>;<br/><span class="kw">hence </span><a NAME="E4:150_1_1_3"/>
( <font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c6">x</font> is  <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a>  &amp; <font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c6">x</font> is  <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a>  &amp; <font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c6">x</font> is  <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a>  &amp; <font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c6">x</font> is  <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a>  &amp; <font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c6">x</font> is  <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a>  &amp; <font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c6">x</font> is  <a href="glib_003.html#V11" title="GLIB_003:attr.11">real-WEV</a>  &amp; <font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c6">x</font> is  <a href="glib_003.html#V8" title="GLIB_003:attr.8">nonnegative-weighted</a>  &amp; <font color="Maroon" title="c5">F</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c6">x</font> is  <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</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><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E16:150_1_1"/>
( <font color="Maroon" title="c5">F</font> is  <a href="glib_000.html#V14" title="GLIB_000:attr.14">finite</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_000.html#V15" title="GLIB_000:attr.15">loopless</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_000.html#V16" title="GLIB_000:attr.16">trivial</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_000.html#V18" title="GLIB_000:attr.18">non-multi</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_000.html#V20" title="GLIB_000:attr.20">simple</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_003.html#V19" title="GLIB_003:attr.19">real-WEV</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_003.html#V16" title="GLIB_003:attr.16">nonnegative-weighted</a>  &amp; <font color="Maroon" title="c5">F</font> is  <a href="glib_002.html#V8" title="GLIB_002:attr.8">Tree-like</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_003.html#D28" target="_self" title="GLIB_003:def.28">Def28</a>, <a class="ref" href="glib_003.html#D31" target="_self" title="GLIB_003:def.31">Def31</a>, <a class="ref" href="glib_000.html#D60" title="GLIB_000:def.60">GLIB_000:def 60</a>, <a class="ref" href="glib_000.html#D61" title="GLIB_000:def.61">GLIB_000:def 61</a>, <a class="ref" href="glib_000.html#D62" title="GLIB_000:def.62">GLIB_000:def 62</a>, <a class="ref" href="glib_000.html#D64" title="GLIB_000:def.64">GLIB_000:def 64</a>, <a class="ref" href="glib_000.html#D66" title="GLIB_000:def.66">GLIB_000:def 66</a>, <a class="ref" href="glib_002.html#D14" title="GLIB_002:def.14">GLIB_002:def 14</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/>


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