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

<b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">F</font> be   <a href="afinsq_1.html#NM2">XFinSequence</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">G</font> be   <a href="afinsq_1.html#NM2">XFinSequence</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">D</font>;<br/>







<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="afinsq_1.html#NM2">XFinSequence</a> of <font color="Maroon">D</font>] <b>means </b>for <font color="Olive">F</font> being  <a href="afinsq_1.html#NM2">XFinSequence</a> of <font color="Maroon">D</font><br/> for <font color="Olive">b</font> being  <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">D</font>  st <font color="Olive">b</font> is <a href="binop_1.html#V2">associative</a> &amp; ( <font color="Olive">b</font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  or (  <a href="afinsq_1.html#K1">len</a> <font color="Olive">F</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp;  <a href="afinsq_1.html#K1">len</a> <font color="Maroon">a<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 ) ) holds <br/><font color="Olive">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p1">(<span class="default"><font color="Olive">F</font> <a href="afinsq_1.html#K5">^</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Olive">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <font color="Olive">F</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <font color="Maroon">a<sub>1</sub></font></span>)</span>;<br/>
<a NAME="E1:59"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="afinsq_1.html#K4">&lt;%&gt;</a> <font color="Maroon">D</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">F</font> be   <a href="afinsq_1.html#NM2">XFinSequence</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">D</font>;<br/>



<b>assume </b><a NAME="E1:59_1"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">b</font> is <a href="binop_1.html#V2">associative</a> &amp; ( <font color="Maroon">b</font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  or (  <a href="afinsq_1.html#K1">len</a> <font color="Maroon">F</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp;  <a href="afinsq_1.html#K1">len</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K4">&lt;%&gt;</a> <font color="Maroon">D</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 ) ) )
 ;<br/>

<b>thus </b><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="afinsq_1.html#K5">^</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K4">&lt;%&gt;</a> <font color="Maroon">D</font></span>)</span></span>)</span> = 
<font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <font color="Maroon">F</font>
<b>by </b><i><a class="ref" href="afinsq_1.html#T32">AFINSQ_1:32</a></i>
<br/>.= 
<font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <font color="Maroon">F</font></span>)</span>,<span class="p1">(<span class="default"><a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="ref" href="stirl2_1.html#T6" target="_self">Th6</a>, , <a class="ref" href="setwiseo.html#T23">SETWISEO:23</a></i>
<br/>.= 
<font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <font color="Maroon">F</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K4">&lt;%&gt;</a> <font color="Maroon">D</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="stirl2_1.html#T6" target="_self">Th6</a>, <a class="ref" href="stirl2_1.html#T2" target="_self">Th2</a>, <a class="ref" href="card_1.html#T47">CARD_1:47</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E2:59"/><i><font color="Green">E40</font></i>: 
for <font color="Olive">G</font> being  <a href="afinsq_1.html#NM2">XFinSequence</a> of <font color="Maroon">D</font><br/> for <font color="Olive">d</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">G</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">G</font> <a href="afinsq_1.html#K5">^</a> <span class="p1"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Olive">d</font></span><a href="afinsq_1.html#K9">%&gt;</a></span>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">G</font> be   <a href="afinsq_1.html#NM2">XFinSequence</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">d</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>;<br/>



<b>assume </b><a NAME="E1:59_2"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">G</font>]
 ;<br/>

<b>let </b><font color="Maroon">F</font> be   <a href="afinsq_1.html#NM2">XFinSequence</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">D</font>;<br/>



<b>assume </b><a NAME="E2:59_2"/><i><font color="Green">E58</font></i>: 
( <font color="Maroon">b</font> is <a href="binop_1.html#V2">associative</a> &amp; ( <font color="Maroon">b</font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  or (  <a href="afinsq_1.html#K1">len</a> <font color="Maroon">F</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp;  <a href="afinsq_1.html#K1">len</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="afinsq_1.html#K5">^</a> <span class="p2"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">d</font></span><a href="afinsq_1.html#K9">%&gt;</a></span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 ) ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:59_2_1_1"/>
(  <a href="afinsq_1.html#K1">len</a> <font color="Maroon">G</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 or  <a href="afinsq_1.html#K1">len</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_2_1_1_1"><b>suppose </b></a><a NAME="E1:59_2_1_1_1"/><i><font color="Green">E62</font></i>: 
 <a href="afinsq_1.html#K1">len</a> <font color="Maroon">G</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:59_2_1_1_1"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="afinsq_1.html#K5">^</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="afinsq_1.html#K5">^</a> <span class="p3"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">d</font></span><a href="afinsq_1.html#K9">%&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="afinsq_1.html#K5">^</a> <font color="Maroon">G</font></span>)</span></span>)</span>,<font color="Maroon">d</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_2_1_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:59_2_1_1_1_1"/>
 <a href="afinsq_1.html#K1">len</a> <font color="Maroon">G</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="stirl2_1.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E2:59_2_1_1_1_1"/><b>then </b>
( <font color="Maroon">b</font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  or (  <a href="afinsq_1.html#K1">len</a> <font color="Maroon">F</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp;  <a href="afinsq_1.html#K1">len</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="afinsq_1.html#K5">^</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1">len</a> <font color="Maroon">F</font></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1">len</a> <font color="Maroon">G</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="afinsq_1.html#K1">len</a> <font color="Maroon">F</font></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1">len</a> <font color="Maroon">G</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1">len</a> <font color="Maroon">F</font></span>)</span> <a href="binop_2.html#K23">+</a> 0 ) )
 
<b>by </b><i>, <a class="ref" href="afinsq_1.html#T20">AFINSQ_1:20</a>, <a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/>
<a NAME="E3:59_2_1_1_1_1"/><b>then </b>
<font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="afinsq_1.html#K5">^</a> <font color="Maroon">G</font></span>)</span></span>)</span>,<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="afinsq_1.html#K5">^</a> <font color="Maroon">G</font></span>)</span> <a href="afinsq_1.html#K5">^</a> <span class="p2"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">d</font></span><a href="afinsq_1.html#K9">%&gt;</a></span></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:59_2_1_1_1_1"/>
<font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="afinsq_1.html#K5">^</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="afinsq_1.html#K5">^</a> <span class="p3"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">d</font></span><a href="afinsq_1.html#K9">%&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="afinsq_1.html#K5">^</a> <font color="Maroon">G</font></span>)</span></span>)</span>,<font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="afinsq_1.html#T30">AFINSQ_1:30</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:59_2_1_1_1"/><i><font color="Green">E65</font></i>: 
 <a href="afinsq_1.html#K1">len</a> <font color="Maroon">G</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i><a class="ref" href="stirl2_1.html#T10" target="_self">Th10</a>, <a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/><b>then </b><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="afinsq_1.html#K5">^</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="afinsq_1.html#K5">^</a> <span class="p3"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">d</font></span><a href="afinsq_1.html#K9">%&gt;</a></span></span>)</span></span>)</span> = 
<font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <font color="Maroon">F</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <font color="Maroon">G</font></span>)</span></span>)</span>,<font color="Maroon">d</font>
<b>by </b><i><a class="ref" href="stirl2_1.html#T8" target="_self">Th8</a>, , <a class="ref" href="stirl2_1.html#T12" target="_self">Th12</a></i>
<br/>.= 
<font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <font color="Maroon">F</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <font color="Maroon">G</font></span>)</span>,<font color="Maroon">d</font></span>)</span>
<b>by </b><i>, <a class="ref" href="binop_1.html#D3">BINOP_1:def 3</a></i>
<br/>.= 
<font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <font color="Maroon">F</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="afinsq_1.html#K5">^</a> <span class="p3"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">d</font></span><a href="afinsq_1.html#K9">%&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="stirl2_1.html#E1:59_2"><i><font color="Green">E47</font></i></a>, </i>
;<br/><b>hence </b><a NAME="E5:59_2_1_1_1"/>
<font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="afinsq_1.html#K5">^</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="afinsq_1.html#K5">^</a> <span class="p3"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">d</font></span><a href="afinsq_1.html#K9">%&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <font color="Maroon">F</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="afinsq_1.html#K5">^</a> <span class="p3"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">d</font></span><a href="afinsq_1.html#K9">%&gt;</a></span></span>)</span></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_2_1_1_2"><b>suppose </b></a><a NAME="E1:59_2_1_1_2"/>
 <a href="afinsq_1.html#K1">len</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:59_2_1_1_2"/><b>then </b><i><font color="Green">E67</font></i>: 
<font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i/>;<br/><b>hence </b><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="afinsq_1.html#K5">^</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="afinsq_1.html#K5">^</a> <span class="p3"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">d</font></span><a href="afinsq_1.html#K9">%&gt;</a></span></span>)</span></span>)</span> = 
<font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="afinsq_1.html#K5">^</a> <span class="p2"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">d</font></span><a href="afinsq_1.html#K9">%&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="afinsq_1.html#T32">AFINSQ_1:32</a></i>
<br/>.= 
<font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <font color="Maroon">F</font></span>)</span>,<font color="Maroon">d</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <font color="Maroon">F</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p2"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">d</font></span><a href="afinsq_1.html#K9">%&gt;</a></span></span>)</span>
<b>by </b><i><a class="txt" href="stirl2_1.html#E1:59"><i><font color="Green">E38</font></i></a></i>
<br/>.= 
<font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <font color="Maroon">F</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="afinsq_1.html#K5">^</a> <span class="p3"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">d</font></span><a href="afinsq_1.html#K9">%&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="stirl2_1.html#T10" target="_self">Th10</a>, <a class="ref" href="afinsq_1.html#T32">AFINSQ_1:32</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:59_2"/>
<font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="afinsq_1.html#K5">^</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="afinsq_1.html#K5">^</a> <span class="p3"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">d</font></span><a href="afinsq_1.html#K9">%&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <font color="Maroon">F</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="afinsq_1.html#K5">^</a> <span class="p3"><a href="afinsq_1.html#K9">&lt;%</a><span class="default"><font color="Maroon">d</font></span><a href="afinsq_1.html#K9">%&gt;</a></span></span>)</span></span>)</span>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E3:59"/>
for <font color="Olive">G</font> being  <a href="afinsq_1.html#NM2">XFinSequence</a> of <font color="Maroon">D</font> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">G</font>]
 
<b>from </b><i><a class="ref" href="stirl2_1.html#S5" target="_self">STIRL2_1:sch 5</a>(<a class="ref" href="stirl2_1.html#T5" target="_self">Th5</a>, <a class="ref" href="stirl2_1.html#T6" target="_self">Th6</a>);<br/></i>
<b>hence </b><a NAME="E4:59"/>
( <font color="Maroon">b</font> is <a href="binop_1.html#V2">associative</a> &amp; ( <font color="Maroon">b</font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  or (  <a href="afinsq_1.html#K1">len</a> <font color="Maroon">F</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp;  <a href="afinsq_1.html#K1">len</a> <font color="Maroon">G</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 ) ) implies <font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="afinsq_1.html#K5">^</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <font color="Maroon">F</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="stirl2_1.html#K4" target="_self">"**"</a> <font color="Maroon">G</font></span>)</span> )
 ;<br/>


</div>
