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<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">D</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">z</font> be    <a href="finseq_2.html#M2" target="_self">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="finseq_2.html#K4" target="_self">-tuples_on</a> <font color="Maroon">D</font>;<br/>





<b>consider </b><font color="Maroon">t</font> being    <a href="finseq_2.html#M2" target="_self">Element</a> of <font color="Maroon">i</font> <a href="finseq_2.html#K4" target="_self">-tuples_on</a> <font color="Maroon">D</font>, <font color="Maroon">s</font> being    <a href="finseq_2.html#M2" target="_self">Element</a> of 1 <a href="finseq_2.html#K4" target="_self">-tuples_on</a> <font color="Maroon">D</font><b> such that </b><br/><a NAME="E2:137"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">s</font>
 <b>by </b><i><a class="ref" href="finseq_2.html#T34" target="_self">Th34</a></i>;<br/>
<a NAME="E3:137"/>
 ex <font color="Olive">d</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> st <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">d</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T27" target="_self">Th27</a></i>;<br/>
<b>hence </b><a NAME="E4:137"/>
 ex <font color="Olive">t</font> being   <a href="finseq_2.html#M2" target="_self">Element</a> of <font color="Maroon">i</font> <a href="finseq_2.html#K4" target="_self">-tuples_on</a> <font color="Maroon">D</font> ex <font color="Olive">d</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font> st <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">d</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="finseq_2.html#T36" target="_self">Th36</a></i>;<br/>


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