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<b>let </b><font color="Maroon">A</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">a</font> be   <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><a href="altcat_1.html#K7">EnsCat</a> <font color="Maroon">A</font></span>)</span>;<br/>



<a NAME="E1:62"/>
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">a</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">a</font>,<font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="altcat_1.html#D16">ALTCAT_1:def 16</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">e</font> =  <a href="partfun1.html#K6">id</a> <font color="Maroon">a</font> as   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">a</font>,<font color="Maroon">a</font> <b>by </b><i><a class="ref" href="altcat_1.html#T2">ALTCAT_1:2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">b</font> be   <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><a href="altcat_1.html#K7">EnsCat</a> <font color="Maroon">A</font></span>)</span>;<br/><b>assume </b><a NAME="E1:62_1"/><i><font color="Green">E35</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/><a NAME="E2:62_1"/><i><font color="Green">E36</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="altcat_1.html#D16">ALTCAT_1:def 16</a></i>;<br/><b>then reconsider </b><font color="Maroon">g</font> = <font color="Maroon">f</font> as   <a href="funct_1.html#NM1">Function</a> <b>by </b><i>, </i>;<br/><i><font color="Green">E39</font></i>:  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font> = 
 <a href="funct_5.html#K1">proj1</a> <font color="Maroon">f</font>
<b>by </b><i><a class="ref" href="funct_5.html#T21">FUNCT_5:21</a></i>
<br/>.= 
<font color="Maroon">a</font>
<b>by </b><i>, , </i>
;<br/><b>thus </b><font color="Maroon">f</font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">e</font> = 
<font color="Maroon">g</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i>, <a class="ref" href="altcat_1.html#D14">ALTCAT_1:def 14</a></i>
<br/>.= 
<font color="Maroon">f</font>
<b>by </b><i>, <a class="ref" href="relat_1.html#T78">RELAT_1:78</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:62"/>
 <a href="altcat_1.html#K8">idm</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="partfun1.html#K6">id</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="altcat_1.html#D19">ALTCAT_1:def 19</a></i>;<br/>


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