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

<b>let </b><font color="Maroon">f</font> be   <a href="binop_1.html#NM1">UnOp</a> of  <a href="midsp_1.html#K13" target="_self">setvect</a> <font color="Maroon">M</font>, <font color="Maroon">g</font> be   <a href="binop_1.html#NM1">UnOp</a> of  <a href="midsp_1.html#K13" target="_self">setvect</a> <font color="Maroon">M</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:69_1_2"/><i><font color="Green">E63</font></i>: 
for <font color="Olive">W</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="midsp_1.html#K13" target="_self">setvect</a> <font color="Maroon">M</font> holds  <font color="Olive">W</font> <a href="midsp_1.html#K14" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">W</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="midsp_1.html#K9" target="_self">ID</a> <font color="Maroon">M</font>
 <b>and </b><br/><a NAME="E2:69_1_2"/><i><font color="Green">E76</font></i>: 
for <font color="Olive">W</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="midsp_1.html#K13" target="_self">setvect</a> <font color="Maroon">M</font> holds  <font color="Olive">W</font> <a href="midsp_1.html#K14" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">W</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="midsp_1.html#K9" target="_self">ID</a> <font color="Maroon">M</font>
 ;<br/>

<a NAME="E3:69_1_2"/>
for <font color="Olive">W</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="midsp_1.html#K13" target="_self">setvect</a> <font color="Maroon">M</font> holds  <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">W</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">W</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">W</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="midsp_1.html#K13" target="_self">setvect</a> <font color="Maroon">M</font>;<br/>

<a NAME="E1:69_1_2_1"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">W</font> <a href="midsp_1.html#K14" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">W</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="midsp_1.html#K9" target="_self">ID</a> <font color="Maroon">M</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:69_1_2_1"/>
<font color="Maroon">W</font> <a href="midsp_1.html#K14" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">W</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="midsp_1.html#K9" target="_self">ID</a> <font color="Maroon">M</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:69_1_2_1"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">W</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:69_1_2"/>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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