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<div class="add">

<b>consider </b><font color="Maroon" title="c1">G1</font> being  <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> non <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a> <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a> <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/>
<b>set </b><font color="Maroon" title="c2">W</font> = <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ;<br/>
<a NAME="E2:88_2_1"/><i><font color="Green" title="E16">A4</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</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">G1</font> &amp;  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">W</font> = <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G1</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <b>by </b><i><a class="ref" href="funct_2.html#T4" title="FUNCT_2:th.4">FUNCT_2:4</a></i>;<br/>
<b>set </b><font color="Maroon" title="c4">G2</font> = <font color="Maroon" title="c1">G1</font> <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="c3">W</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">EL</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <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">G1</font> <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="c3">W</font></span>)</span>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <b>by </b><i><a class="ref" href="relset_1.html#T25" title="RELSET_1:th.25">RELSET_1:25</a></i>;<br/>
<b>set </b><font color="Maroon" title="c6">G3</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">VL</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <b>by </b><i><a class="ref" href="relset_1.html#T25" title="RELSET_1:th.25">RELSET_1:25</a></i>;<br/>
<b>set </b><font color="Maroon" title="c8">G4</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c7">VL</font>;<br/>
<b>take </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c7">VL</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c7">VL</font> is <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> &amp; not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c7">VL</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c7">VL</font> is <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c7">VL</font> is <a href="glib_003.html#V8" title="GLIB_003:attr.8">nonnegative-weighted</a> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c7">VL</font> is <a href="glib_003.html#V11" title="GLIB_003:attr.11">real-WEV</a> )</span><br/>

<b>thus </b><a NAME="E6:88_2_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c7">VL</font> is <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> &amp; not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c7">VL</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c7">VL</font> is <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c7">VL</font> is <a href="glib_003.html#V8" title="GLIB_003:attr.8">nonnegative-weighted</a> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c7">VL</font> is <a href="glib_003.html#V11" title="GLIB_003:attr.11">real-WEV</a> )</span><br/>

<i><font color="Green" title="E17">A5</font></i>:  <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"><span class="p3">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c7">VL</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> 
<b>by </b><i><a class="ref" href="glib_000.html#T12" title="GLIB_000:th.12">GLIB_000:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> 
<b>by </b><i><a class="ref" href="glib_000.html#T12" title="GLIB_000:th.12">GLIB_000:12</a></i>
<br/>.= 
<font color="Maroon" title="c3">W</font>
<b>by </b><i><a class="ref" href="glib_000.html#T11" title="GLIB_000:th.11">GLIB_000:11</a></i>
;<br/>
<a NAME="E8:88_2_1"/><b>then </b><i><font color="Green" title="E18">A6</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c7">VL</font> is <a href="glib_003.html#V7" title="GLIB_003:attr.7">real-weighted</a>
 
<b>by </b><i><a class="ref" href="glib_003.html#D13" target="_self" title="GLIB_003:def.13">Def13</a></i>;<br/>
 <a href="glib_003.html#K6" title="GLIB_003:func.6">the_ELabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c7">VL</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> 
<b>by </b><i><a class="ref" href="glib_000.html#T12" title="GLIB_000:th.12">GLIB_000:12</a></i>
<br/>.= 
<font color="Maroon" title="c5">EL</font>
<b>by </b><i><a class="ref" href="glib_000.html#T11" title="GLIB_000:th.11">GLIB_000:11</a></i>
;<br/>
<a NAME="E10:88_2_1"/><b>then </b><i><font color="Green" title="E19">A7</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c7">VL</font> is <a href="glib_003.html#V9" title="GLIB_003:attr.9">real-elabeled</a>
 
<b>by </b><i><a class="ref" href="glib_003.html#D15" target="_self" title="GLIB_003:def.15">Def15</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="88_2_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">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="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> implies <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_5.html#K8" title="GRAPH_5:func.8">Real&gt;=0</a>  )</span><br/><b>assume </b><a NAME="E1:88_2_1_3"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_5.html#K8" title="GRAPH_5:func.8">Real&gt;=0</a> </span><br/><a NAME="E2:88_2_1_3"/><b>then </b>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:88_2_1_3"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_5.html#K8" title="GRAPH_5:func.8">Real&gt;=0</a> 
 <b>by </b><i><a class="ref" href="graph_5.html#D12" title="GRAPH_5:def.12">GRAPH_5:def 12</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="E12:88_2_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graph_5.html#K8" title="GRAPH_5:func.8">Real&gt;=0</a> 
 
<b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<a NAME="E13:88_2_1"/><b>then </b>
 <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c3">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graph_5.html#K8" title="GRAPH_5:func.8">Real&gt;=0</a> 
 
<b>by </b><i><a class="txt" href="#E2:88_2_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E14:88_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c7">VL</font> is <a href="glib_003.html#V8" title="GLIB_003:attr.8">nonnegative-weighted</a>
 <b>by </b><i><a class="txt" href="#E7:88_2_1"><i><font color="Green" title="E17">A5</font></i></a>, <a class="ref" href="glib_003.html#D14" target="_self" title="GLIB_003:def.14">Def14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c7">VL</font> is <a href="glib_003.html#V11" title="GLIB_003:attr.11">real-WEV</a></span><br/>

<b>thus </b><a NAME="E15:88_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <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="c3">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c7">VL</font> is <a href="glib_003.html#V11" title="GLIB_003:attr.11">real-WEV</a>
 <b>by </b><i><a class="txt" href="#E8:88_2_1"><i><font color="Green" title="E18">A6</font></i></a>, <a class="txt" href="#E10:88_2_1"><i><font color="Green" title="E19">A7</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/>


</div>
