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<b>let </b><font color="Maroon" title="c1">m1</font>, <font color="Maroon" title="c2">m2</font> be  <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a> <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">m2</font> implies for <font color="Olive" title="b1">k</font> being <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Olive" title="b1">k</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> <font color="Maroon" title="c1">m1</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c2">m2</font></span>)</span> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m2</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Olive" title="b1">k</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:14"/><i><font color="Green" title="E9">AS1</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">m2</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">k</font> being <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Olive" title="b1">k</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> <font color="Maroon" title="c1">m1</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c2">m2</font></span>)</span> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m2</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Olive" title="b1">k</font></span>)</span></span><br/>

<b>let </b><font color="Maroon" title="c3">k'</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">k'</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> <font color="Maroon" title="c1">m1</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c2">m2</font></span>)</span> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m2</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E2:14"/><i><font color="Green" title="E10">AS2</font></i>: 
<font color="Maroon" title="c3">k'</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> <font color="Maroon" title="c1">m1</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"><font color="Maroon" title="c1">m1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c2">m2</font></span>)</span> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m2</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span></span><br/>

<b>set </b><font color="Maroon" title="c4">p</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c2">m2</font></span>)</span> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font>;<br/>
<b>set </b><font color="Maroon" title="c5">q</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m2</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span>;<br/>
<a NAME="E3:14"/><i><font color="Green" title="E11">H</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="c1">m1</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k'</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m2</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k'</font> )
 
<b>by </b><i><a class="txt" href="int_6.html#E1:14"><i><font color="Green" title="E9">AS1</font></i></a>, <a class="txt" href="int_6.html#E2:14"><i><font color="Green" title="E10">AS2</font></i></a>, <a class="ref" href="finseq_1.html#T80" title="FINSEQ_1:th.80">FINSEQ_1:80</a></i>;<br/>
<a NAME="E4:14"/>
<font color="Maroon" title="c3">k'</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="c1">m1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c2">m2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="int_6.html#E1:14"><i><font color="Green" title="E9">AS1</font></i></a>, <a class="txt" href="int_6.html#E2:14"><i><font color="Green" title="E10">AS2</font></i></a>, <a class="txt" href="int_6.html#E7"><i><font color="Green" title="E7">length3</font></i></a></i>;<br/>
<a NAME="E5:14"/><b>then </b><i><font color="Green" title="E12">A</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c2">m2</font></span>)</span> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k'</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">m2</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k'</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T80" title="FINSEQ_1:th.80">FINSEQ_1:80</a>, <a class="txt" href="int_6.html#E3:14"><i><font color="Green" title="E11">H</font></i></a>, <a class="txt" href="int_6.html#E7"><i><font color="Green" title="E7">length3</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">k</font> = <font color="Maroon" title="c3">k'</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>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">j</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="c7">j</font> &amp; <font color="Maroon" title="c7">j</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"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c2">m2</font></span>)</span> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c2">m2</font></span>)</span> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">m2</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font> )</span><br/><b>assume </b><a NAME="E1:14_1"/><i><font color="Green" title="E13">B1</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">j</font> &amp; <font color="Maroon" title="c7">j</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"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c2">m2</font></span>)</span> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></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"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c2">m2</font></span>)</span> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">m2</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font></span><br/><a NAME="E2:14_1"/><b>then </b><i><font color="Green" title="E14">B2</font></i>: 
<font color="Maroon" title="c7">j</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"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c2">m2</font></span>)</span> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><a NAME="E3:14_1"/><i><font color="Green" title="E15">AA</font></i>: 
<font color="Maroon" title="c7">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/><a NAME="E4:14_1"/><b>then </b><i><font color="Green" title="E16">D</font></i>: 
<font color="Maroon" title="c7">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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="int_6.html#E1:14_1"><i><font color="Green" title="E13">B1</font></i></a>, <a class="txt" href="int_6.html#E5:14"><i><font color="Green" title="E12">A</font></i></a></i>;<br/><a NAME="E5:14_1"/><i><font color="Green" title="E17">E</font></i>: 
<font color="Maroon" title="c7">j</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> <font color="Maroon" title="c1">m1</font>
 <b>by </b><i><a class="txt" href="int_6.html#E1:14_1"><i><font color="Green" title="E13">B1</font></i></a>, <a class="txt" href="int_6.html#E5:14"><i><font color="Green" title="E12">A</font></i></a>, <a class="txt" href="int_6.html#E2:14"><i><font color="Green" title="E10">AS2</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E6:14_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c2">m2</font></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> <font color="Maroon" title="c1">m1</font>
 <b>by </b><i><a class="txt" href="int_6.html#E1:14"><i><font color="Green" title="E9">AS1</font></i></a>, <a class="txt" href="int_6.html#E7"><i><font color="Green" title="E7">length3</font></i></a></i>;<br/><a NAME="E7:14_1"/><b>then </b>
<font color="Maroon" title="c7">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c2">m2</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="int_6.html#E3:14_1"><i><font color="Green" title="E15">AA</font></i></a>, <a class="txt" href="int_6.html#E5:14_1"><i><font color="Green" title="E17">E</font></i></a>, <a class="txt" href="int_6.html#E1:14_1"><i><font color="Green" title="E13">B1</font></i></a></i>;<br/><a NAME="E8:14_1"/><b>then </b><i><font color="Green" title="E18">B3</font></i>: 
<font color="Maroon" title="c7">j</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="c1">m1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c2">m2</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E9:14_1"/><i><font color="Green" title="E19">B6</font></i>: 
<font color="Maroon" title="c7">j</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="c1">m1</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c6">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="int_6.html#E4:14_1"><i><font color="Green" title="E16">D</font></i></a>, <a class="txt" href="int_6.html#E3:14"><i><font color="Green" title="E11">H</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E10:14_1"/><i><font color="Green" title="E20">B7</font></i>: 
<font color="Maroon" title="c7">j</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">m2</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c6">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="int_6.html#E4:14_1"><i><font color="Green" title="E16">D</font></i></a>, <a class="txt" href="int_6.html#E3:14"><i><font color="Green" title="E11">H</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E11:14_1"/><i><font color="Green" title="E21">B8</font></i>: 
<font color="Maroon" title="c7">j</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"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">m2</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="int_6.html#E4:14_1"><i><font color="Green" title="E16">D</font></i></a>, <a class="txt" href="int_6.html#E5:14"><i><font color="Green" title="E12">A</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c2">m2</font></span>)</span> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c2">m2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font>
<b>by </b><i><a class="txt" href="int_6.html#E2:14_1"><i><font color="Green" title="E14">B2</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font></span>)</span>
<b>by </b><i><a class="txt" href="int_6.html#E8:14_1"><i><font color="Green" title="E18">B3</font></i></a>, <a class="ref" href="valued_1.html#D4" title="VALUED_1:def.4">VALUED_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font></span>)</span>
<b>by </b><i><a class="txt" href="int_6.html#E9:14_1"><i><font color="Green" title="E19">B6</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">m2</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font></span>)</span>
<b>by </b><i><a class="txt" href="int_6.html#E10:14_1"><i><font color="Green" title="E20">B7</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">m2</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font>
<b>by </b><i><a class="txt" href="int_6.html#E11:14_1"><i><font color="Green" title="E21">B8</font></i></a>, <a class="ref" href="valued_1.html#D4" title="VALUED_1:def.4">VALUED_1:def 4</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="E8:14"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c2">m2</font></span>)</span> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m1</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m2</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c3">k'</font></span>)</span>
 <b>by </b><i><a class="txt" href="int_6.html#E5:14"><i><font color="Green" title="E12">A</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>
