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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">j</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">s</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> <font color="Maroon">j</font></span>)</span> <a href="finseq_2.html#K4" target="_self">-tuples_on</a> <font color="Maroon">D</font>;<br/>







<a NAME="E1:126"/>
<font color="Maroon">s</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span> <a href="finseq_2.html#K4" target="_self">-tuples_on</a> <font color="Maroon">D</font>
 
;<br/>
<a NAME="E2:126"/><b>then </b>
<font color="Maroon">s</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">z</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">t</font></span>)</span> where <font color="Olive">z</font> is    <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="Olive">t</font> is    <a href="finseq_2.html#M2" target="_self">Element</a> of <font color="Maroon">j</font> <a href="finseq_2.html#K4" target="_self">-tuples_on</a> <font color="Maroon">D</font> : verum </span>}</span> 
 
<b>by </b><i><a class="ref" href="finseq_2.html#T33" target="_self">Th33</a></i>;<br/>
<b>hence </b><a NAME="E3:126"/>
 ex <font color="Olive">z</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">t</font> being   <a href="finseq_2.html#M2" target="_self">Element</a> of <font color="Maroon">j</font> <a href="finseq_2.html#K4" target="_self">-tuples_on</a> <font color="Maroon">D</font> st <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Olive">z</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">t</font>
 ;<br/>


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