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<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="glib_003.html#V7" title="GLIB_003:attr.7">real-weighted</a> <a href="glib_003.html#NM1" title="GLIB_003:NM.1">WGraph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">W1</font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font><br/> for <font color="Olive" title="b2">W2</font> being   <a href="glib_001.html#M4" title="GLIB_001:mode.4">Subwalk</a> of <font color="Olive" title="b1">W1</font>  ex <font color="Olive" title="b3">ws</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">W1</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a> </span>)</span> st <font color="Olive" title="b2">W2</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_003.html#K1" title="GLIB_003:func.1">Seq</a> <font color="Olive" title="b3">ws</font></span><br/><b>let </b><font color="Maroon" title="c2">W1</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">W2</font> being   <a href="glib_001.html#M4" title="GLIB_001:mode.4">Subwalk</a> of <font color="Maroon" title="c2">W1</font>  ex <font color="Olive" title="b2">ws</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a> </span>)</span> st <font color="Olive" title="b1">W2</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_003.html#K1" title="GLIB_003:func.1">Seq</a> <font color="Olive" title="b2">ws</font></span><br/><b>let </b><font color="Maroon" title="c3">W2</font> be    <a href="glib_001.html#M4" title="GLIB_001:mode.4">Subwalk</a> of <font color="Maroon" title="c2">W1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">ws</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a> </span>)</span> st <font color="Maroon" title="c3">W2</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_003.html#K1" title="GLIB_003:func.1">Seq</a> <font color="Olive" title="b1">ws</font></span><br/>





<b>consider </b><font color="Maroon" title="c4">es</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a> </span>)</span><b> such that </b><br/><a NAME="E2:165"/><i><font color="Green" title="E34">A1</font></i>: 
<font color="Maroon" title="c3">W2</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_003.html#K1" title="GLIB_003:func.1">Seq</a> <font color="Maroon" title="c4">es</font>
 <b>by </b><i><a class="ref" href="glib_001.html#D32" title="GLIB_001:def.32">GLIB_001:def 32</a></i>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <b>-&gt; </b>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  = <span class="p1">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">es</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1</span>)</span>;<br/>
<b>consider </b><font color="Maroon" title="c5">ws</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E4:165"/><i><font color="Green" title="E35">A2</font></i>: 
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">ws</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">es</font> &amp; ( for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">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="c4">es</font> holds <br/><font color="Maroon" title="c5">ws</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>) ) )
 <b>from </b><i><a class="ref" href="funct_1.html#S3" title="FUNCT_1:sch.3">FUNCT_1:sch 3</a>();<br/></i>
<b>consider </b><font color="Maroon" title="c6">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E6:165"/><i><font color="Green" title="E36">A3</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">ws</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c6">k</font>
 <b>by </b><i><a class="txt" href="#E4:165"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="finseq_1.html#D12" title="FINSEQ_1:def.12">FINSEQ_1:def 12</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">ws</font> = <font color="Maroon" title="c5">ws</font> as   <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a> <b>by </b><i><a class="txt" href="#E6:165"><i><font color="Green" title="E36">A3</font></i></a>, <a class="ref" href="finseq_1.html#D12" title="FINSEQ_1:def.12">FINSEQ_1:def 12</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="165_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">z</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="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">ws</font> implies <font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W1</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a>  )</span><br/><b>assume </b><a NAME="E1:165_1"/><i><font color="Green" title="E37">A4</font></i>: 
<font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">ws</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W1</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a> </span><br/><b>then consider </b><font color="Maroon" title="c9">x</font>, <font color="Maroon" title="c10">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:165_1"/><i><font color="Green" title="E38">A5</font></i>: 
<font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">x</font>,<font color="Maroon" title="c10">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#D1" title="RELAT_1:def.1">RELAT_1:def 1</a></i>;<br/><a NAME="E4:165_1"/><i><font color="Green" title="E39">A6</font></i>: 
( <font color="Maroon" title="c9">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="c4">es</font> &amp; <font color="Maroon" title="c7">ws</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">y</font> )
 <b>by </b><i><a class="txt" href="#E4:165"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="#E1:165_1"><i><font color="Green" title="E37">A4</font></i></a>, <a class="txt" href="#E3:165_1"><i><font color="Green" title="E38">A5</font></i></a>, <a class="ref" href="funct_1.html#T8" title="FUNCT_1:th.8">FUNCT_1:8</a></i>;<br/><a NAME="E5:165_1"/><b>then </b><i><font color="Green" title="E40">A7</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">es</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">es</font>
 <b>by </b><i><a class="ref" href="funct_1.html#T8" title="FUNCT_1:th.8">FUNCT_1:8</a></i>;<br/><a NAME="E6:165_1"/><b>then </b><i><font color="Green" title="E41">A8</font></i>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a> </span>)</span>
 <b>by </b><i><a class="ref" href="funct_1.html#T8" title="FUNCT_1:th.8">FUNCT_1:8</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c11">x</font> = <font color="Maroon" title="c9">x</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/><a NAME="E8:165_1"/><i><font color="Green" title="E42">A9</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">x</font> &amp; <font color="Maroon" title="c11">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="#E6:165_1"><i><font color="Green" title="E41">A8</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><a NAME="E9:165_1"/><b>then </b><i><font color="Green" title="E43">A10</font></i>: 
<font color="Maroon" title="c11">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a> </span>)</span>
 <b>by </b><i><a class="ref" href="glib_003.html#D18" target="_self" title="GLIB_003:def.18">Def18</a></i>;<br/><a NAME="E10:165_1"/><b>then </b>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a> </span>)</span>
 <b>by </b><i><a class="txt" href="#E8:165_1"><i><font color="Green" title="E42">A9</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><a NAME="E11:165_1"/><b>then </b><i><font color="Green" title="E44">A11</font></i>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c11">x</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a> </span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W1</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a> 
 <b>by </b><i><a class="ref" href="funct_1.html#T8" title="FUNCT_1:th.8">FUNCT_1:8</a></i>;<br/><a NAME="E12:165_1"/><i><font color="Green" title="E45">A12</font></i>: 
<font color="Maroon" title="c10">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">es</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:165"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="#E4:165_1"><i><font color="Green" title="E39">A6</font></i></a></i>;<br/><a NAME="E13:165_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a> </span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E8:165_1"><i><font color="Green" title="E42">A9</font></i></a>, <a class="txt" href="#E9:165_1"><i><font color="Green" title="E43">A10</font></i></a>, <a class="ref" href="glib_003.html#D18" target="_self" title="GLIB_003:def.18">Def18</a></i>;<br/><b>hence </b><a NAME="E14:165_1"/>
<font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W1</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a> 
 <b>by </b><i><a class="txt" href="#E3:165_1"><i><font color="Green" title="E38">A5</font></i></a>, <a class="txt" href="#E5:165_1"><i><font color="Green" title="E40">A7</font></i></a>, <a class="txt" href="#E11:165_1"><i><font color="Green" title="E44">A11</font></i></a>, <a class="txt" href="#E12:165_1"><i><font color="Green" title="E45">A12</font></i></a>, <a class="ref" href="funct_1.html#T8" title="FUNCT_1:th.8">FUNCT_1:8</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>
<b>then reconsider </b><font color="Maroon" title="c8">ws</font> = <font color="Maroon" title="c7">ws</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a> </span>)</span> <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c8">ws</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">W2</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_003.html#K1" title="GLIB_003:func.1">Seq</a> <font color="Maroon" title="c8">ws</font></span><br/>

<i><font color="Green" title="E37">A13</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="glib_003.html#K1" title="GLIB_003:func.1">Seq</a> <font color="Maroon" title="c4">es</font></span>)</span> = 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">es</font>
<b>by </b><i><a class="ref" href="glib_001.html#T5" title="GLIB_001:th.5">GLIB_001:5</a></i>
<br/>.= 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c8">ws</font></span>)</span>
<b>by </b><i><a class="txt" href="#E4:165"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="pre_circ.html#T21" title="PRE_CIRC:th.21">PRE_CIRC:21</a></i>
<br/>.= 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c8">ws</font>
<b>by </b><i><a class="ref" href="pre_circ.html#T21" title="PRE_CIRC:th.21">PRE_CIRC:21</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="glib_003.html#K1" title="GLIB_003:func.1">Seq</a> <font color="Maroon" title="c8">ws</font></span>)</span>
<b>by </b><i><a class="ref" href="glib_001.html#T5" title="GLIB_001:th.5">GLIB_001:5</a></i>
;<br/>
<a NAME="E11:165"/><b>then </b><i><font color="Green" title="E38">A14</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">W2</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="glib_003.html#K1" title="GLIB_003:func.1">Seq</a> <font color="Maroon" title="c8">ws</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E2:165"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="glib_003.html#D18" target="_self" title="GLIB_003:def.18">Def18</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="165_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">n</font> &amp; <font color="Maroon" title="c9">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">W2</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a> </span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">W2</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a> </span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c9">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_003.html#K1" title="GLIB_003:func.1">Seq</a> <font color="Maroon" title="c8">ws</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c9">n</font> )</span><br/><b>assume </b><a NAME="E1:165_3"/><i><font color="Green" title="E39">A15</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">n</font> &amp; <font color="Maroon" title="c9">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">W2</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a> </span>)</span> )
 ; <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"><font color="Maroon" title="c3">W2</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a> </span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c9">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_003.html#K1" title="GLIB_003:func.1">Seq</a> <font color="Maroon" title="c8">ws</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c9">n</font></span><br/><a NAME="E2:165_3"/><i><font color="Green" title="E40">A16</font></i>: 
 <a href="glib_003.html#K1" title="GLIB_003:func.1">Seq</a> <font color="Maroon" title="c8">ws</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">ws</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">es</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:165"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="finseq_1.html#D14" title="FINSEQ_1:def.14">FINSEQ_1:def 14</a></i>;<br/><a NAME="E3:165_3"/><i><font color="Green" title="E41">A17</font></i>: 
 <a href="glib_003.html#K1" title="GLIB_003:func.1">Seq</a> <font color="Maroon" title="c4">es</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">es</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">es</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D14" title="FINSEQ_1:def.14">FINSEQ_1:def 14</a></i>;<br/><a NAME="E4:165_3"/><i><font color="Green" title="E42">A18</font></i>: 
 <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">es</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">es</font>
 <b>by </b><i><a class="txt" href="#E4:165"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="#E6:165"><i><font color="Green" title="E36">A3</font></i></a>, <a class="ref" href="finseq_1.html#D13" title="FINSEQ_1:def.13">FINSEQ_1:def 13</a></i>;<br/><a NAME="E5:165_3"/><i><font color="Green" title="E43">A19</font></i>: 
<font color="Maroon" title="c9">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K1" title="GLIB_003:func.1">Seq</a> <font color="Maroon" title="c8">ws</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E11:165"><i><font color="Green" title="E38">A14</font></i></a>, <a class="txt" href="#E1:165_3"><i><font color="Green" title="E39">A15</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><a NAME="E6:165_3"/><b>then </b>
<font color="Maroon" title="c9">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">es</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:165_3"><i><font color="Green" title="E40">A16</font></i></a>, <a class="ref" href="funct_1.html#T21" title="FUNCT_1:th.21">FUNCT_1:21</a></i>;<br/><a NAME="E7:165_3"/><b>then </b><i><font color="Green" title="E44">A20</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">es</font></span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c9">n</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="c4">es</font>
 <b>by </b><i><a class="txt" href="#E4:165_3"><i><font color="Green" title="E42">A18</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><a NAME="E8:165_3"/><i><font color="Green" title="E45">A21</font></i>: 
<font color="Maroon" title="c9">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K1" title="GLIB_003:func.1">Seq</a> <font color="Maroon" title="c4">es</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E10:165"><i><font color="Green" title="E37">A13</font></i></a>, <a class="txt" href="#E11:165"><i><font color="Green" title="E38">A14</font></i></a>, <a class="txt" href="#E1:165_3"><i><font color="Green" title="E39">A15</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><span class="p1">(<span class="default"><a href="glib_003.html#K1" title="GLIB_003:func.1">Seq</a> <font color="Maroon" title="c8">ws</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c9">n</font> = 
<font color="Maroon" title="c8">ws</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">es</font></span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c9">n</font></span>)</span>
<b>by </b><i><a class="txt" href="#E2:165_3"><i><font color="Green" title="E40">A16</font></i></a>, <a class="txt" href="#E5:165_3"><i><font color="Green" title="E43">A19</font></i></a>, <a class="ref" href="funct_1.html#T22" title="FUNCT_1:th.22">FUNCT_1:22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">es</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">es</font></span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E4:165"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="#E7:165_3"><i><font color="Green" title="E44">A20</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K1" title="GLIB_003:func.1">Seq</a> <font color="Maroon" title="c4">es</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">n</font></span>)</span>
<b>by </b><i><a class="txt" href="#E3:165_3"><i><font color="Green" title="E41">A17</font></i></a>, <a class="txt" href="#E8:165_3"><i><font color="Green" title="E45">A21</font></i></a>, <a class="ref" href="funct_1.html#T22" title="FUNCT_1:th.22">FUNCT_1:22</a></i>
;<br/><b>hence </b><a NAME="E10:165_3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">W2</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a> </span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c9">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_003.html#K1" title="GLIB_003:func.1">Seq</a> <font color="Maroon" title="c8">ws</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c9">n</font>
 <b>by </b><i><a class="txt" href="#E2:165"><i><font color="Green" title="E34">A1</font></i></a>, <a class="txt" href="#E1:165_3"><i><font color="Green" title="E39">A15</font></i></a>, <a class="ref" href="glib_003.html#D18" target="_self" title="GLIB_003:def.18">Def18</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>
<b>hence </b><a NAME="E13:165"/>
<font color="Maroon" title="c3">W2</font> <a href="glib_003.html#K9" title="GLIB_003:func.9">.weightSeq()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_003.html#K1" title="GLIB_003:func.1">Seq</a> <font color="Maroon" title="c8">ws</font>
 <b>by </b><i><a class="txt" href="#E11:165"><i><font color="Green" title="E38">A14</font></i></a>, <a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</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>
