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<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">f</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">G</font> be   <a href="matrix_1.html#NM1">Matrix</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:5"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E2:5"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">f</font> <a href="goboard1.html#R1">is_sequence_on</a> <font color="Maroon">G</font>
 ;<br/>

<b>consider </b><font color="Maroon">i</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E4:5"/>
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E5:5"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">f</font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">i</font>
 <b>by </b><i>, <a class="ref" href="finseq_5.html#T52">FINSEQ_5:52</a></i>;<br/>
<b>thus </b><a NAME="E6:5"/>
<font color="Maroon">f</font> <a href="finseq_5.html#K2">:-</a> <font color="Maroon">p</font> <a href="goboard1.html#R1">is_sequence_on</a> <font color="Maroon">G</font>
 <b>by </b><i>, , <a class="ref" href="jordan8.html#T5">JORDAN8:5</a></i>;<br/>


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