<?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="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">G</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">H</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">D</font>;<br/>









<b>assume </b><a NAME="E1:25"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">g</font> is <a href="binop_1.html#V2">associative</a> &amp; <font color="Maroon">g</font> is <a href="binop_1.html#V1">commutative</a> &amp; ( <font color="Maroon">g</font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 ) )
 ;<br/>

<a NAME="E2:25"/><i><font color="Green">E37</font></i>: 
(  <a href="finsop_1.html#K5" target="_self">dom</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> &amp;  <a href="finsop_1.html#K5" target="_self">dom</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span> &amp;  <a href="finsop_1.html#K5" target="_self">dom</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E3:25"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> 0 or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/>
<b>hence </b><a NAME="E4:25"/>
(  not  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> or  not  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> or  ex <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5" target="_self">dom</a> <font color="Maroon">F</font> &amp; not <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font></span>)</span> ) or <font color="Maroon">g</font> <a href="finsop_1.html#K2" target="_self">"**"</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="finsop_1.html#K2" target="_self">"**"</a> <font color="Maroon">G</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="finsop_1.html#K2" target="_self">"**"</a> <font color="Maroon">H</font></span>)</span> )
 <b>by </b><i>, , , </i>;<br/>


</div>
