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<b>let </b><font color="Maroon">A</font> be   <a href="waybel_0.html#NM1">prenet</a> of <font color="Maroon">L</font>, <font color="Maroon">B</font> be   <a href="waybel_0.html#NM1">prenet</a> of <font color="Maroon">L</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:29_1_2"/><i><font color="Green">E35</font></i>: 
 ex <font color="Olive">g</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="finsub_1.html#K5">Fin</a> <font color="Maroon">J</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> st <br/>for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> <font color="Maroon">J</font> holds <br/> ( <font color="Olive">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Olive">x</font></span>)</span> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="waybel_0.html#G1">NetStr</a>(# <span class="p1">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">J</font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">J</font></span>)</span></span>)</span>,<font color="Olive">g</font> #) )
 <b>and </b><br/><a NAME="E2:29_1_2"/><i><font color="Green">E36</font></i>: 
 ex <font color="Olive">g</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="finsub_1.html#K5">Fin</a> <font color="Maroon">J</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> st <br/>for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> <font color="Maroon">J</font> holds <br/> ( <font color="Olive">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Olive">x</font></span>)</span> &amp; <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="waybel_0.html#G1">NetStr</a>(# <span class="p1">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">J</font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">J</font></span>)</span></span>)</span>,<font color="Olive">g</font> #) )
 ;<br/>

<b>consider </b><font color="Maroon">g1</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="finsub_1.html#K5">Fin</a> <font color="Maroon">J</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E4:29_1_2"/><i><font color="Green">E56</font></i>: 
for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> <font color="Maroon">J</font> holds <br/> ( <font color="Maroon">g1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Olive">x</font></span>)</span> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="waybel_0.html#G1">NetStr</a>(# <span class="p1">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">J</font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">J</font></span>)</span></span>)</span>,<font color="Maroon">g1</font> #) )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">g2</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="finsub_1.html#K5">Fin</a> <font color="Maroon">J</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E6:29_1_2"/><i><font color="Green">E58</font></i>: 
for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> <font color="Maroon">J</font> holds <br/> ( <font color="Maroon">g2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Olive">x</font></span>)</span> &amp; <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="waybel_0.html#G1">NetStr</a>(# <span class="p1">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">J</font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">J</font></span>)</span></span>)</span>,<font color="Maroon">g2</font> #) )
 <b>by </b><i/>;<br/>
<a NAME="E7:29_1_2"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="finsub_1.html#K5">Fin</a> <font color="Maroon">J</font> holds <br/><font color="Maroon">g1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:29_1_2_1"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="finsub_1.html#K5">Fin</a> <font color="Maroon">J</font>
 ;<br/>

<b>hence </b><font color="Maroon">g1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, </i>
;<br/><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E8:29_1_2"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 <b>by </b><i>, , <a class="ref" href="funct_2.html#T18">FUNCT_2:18</a></i>;<br/>


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