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

<b>set </b><font color="Maroon">e</font> =  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">F</font>;<br/>
<b>let </b><font color="Maroon">u1</font> be   <a href="binop_1.html#NM1">UnOp</a> of <font color="Maroon">D</font>, <font color="Maroon">u2</font> be   <a href="binop_1.html#NM1">UnOp</a> of <font color="Maroon">D</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:72_1_1"/><i><font color="Green">E39</font></i>: 
for <font color="Olive">d</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> holds <br/> ( <font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <font color="Olive">d</font>,<span class="p1">(<span class="default"><font color="Maroon">u1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">d</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">F</font> &amp; <font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">u1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">d</font></span>)</span>,<font color="Olive">d</font> <a href="hidden.html#R1">=</a>  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">F</font> )
 <b>and </b><br/><a NAME="E2:72_1_1"/><i><font color="Green">E51</font></i>: 
for <font color="Olive">d</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> holds <br/> ( <font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <font color="Olive">d</font>,<span class="p1">(<span class="default"><font color="Maroon">u2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">d</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">F</font> &amp; <font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">u2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">d</font></span>)</span>,<font color="Olive">d</font> <a href="hidden.html#R1">=</a>  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">F</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="finseqop.html#D1" target="_self">FINSEQOP:def 1</a><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1_1_1"><b>now </b></a><div class="add"><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>set </b><font color="Maroon">d1</font> = <font color="Maroon">u1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font>;<br/><b>set </b><font color="Maroon">d2</font> = <font color="Maroon">u2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font>;<br/><b>thus </b><font color="Maroon">u1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font> = 
<font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">u1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font></span>)</span>,<span class="p1">(<span class="default"><a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">F</font></span>)</span>
<b>by </b><i><a class="ref" href="finseqop.html#T7" target="_self">Th7</a>, <a class="ref" href="setwiseo.html#T23">SETWISEO:23</a></i>
<br/>.= 
<font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">u1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">d</font>,<span class="p2">(<span class="default"><font color="Maroon">u2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">u1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font></span>)</span>,<font color="Maroon">d</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">u2</font> <a href="funct_2.html#K3">.</a> <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">F</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">F</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">u2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">u2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i><a class="ref" href="finseqop.html#T7" target="_self">Th7</a>, <a class="ref" href="setwiseo.html#T23">SETWISEO:23</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:72_1_1"/>
<font color="Maroon">u1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


</div>
