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<b>let </b><font color="Maroon">a</font> be   <a href="prvect_1.html#NM1">Domain-Sequence</a>;<br/><b>let </b><font color="Maroon">d</font> be   <a href="binop_1.html#NM1">UnOp</a> of  <a href="card_3.html#K4">product</a> <font color="Maroon">a</font>, <font color="Maroon">d'</font> be   <a href="binop_1.html#NM1">UnOp</a> of  <a href="card_3.html#K4">product</a> <font color="Maroon">a</font>;<br/>



<b>assume </b><a NAME="E1:40"/><i><font color="Green">E22</font></i>: 
for <font color="Olive">f</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="card_3.html#K4">product</a> <font color="Maroon">a</font><br/> for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">a</font> holds  <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="funct_2.html#K3">.</a> <font color="Olive">f</font></span>)</span> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">d'</font> <a href="funct_2.html#K3">.</a> <font color="Olive">f</font></span>)</span> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Olive">i</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="40_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">f</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="card_3.html#K4">product</a> <font color="Maroon">a</font>;<br/><a NAME="E1:40_1"/>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">a</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">d'</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">a</font> &amp; ( 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="finseq_1.html#K4">dom</a> <font color="Maroon">a</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">d'</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> ) )
 <b>by </b><i><a class="txt" href="prvect_1.html#E5"><i><font color="Green">Lemma23</font></i></a>, <a class="ref" href="card_3.html#T18">CARD_3:18</a></i>;<br/><b>hence </b><a NAME="E2:40_1"/>
<font color="Maroon">d</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d'</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:40"/>
<font color="Maroon">d</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">d'</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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