<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E27">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: INT_5:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">fr</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   holds <br/>(  ex <font color="Olive" title="b2">d</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( <font color="Olive" title="b2">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b1">fr</font> &amp;  not <font color="Olive" title="b1">fr</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  not <font color="Olive" title="b1">fr</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  not <font color="Olive" title="b1">fr</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 ) or  <a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Olive" title="b1">fr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  <a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Olive" title="b1">fr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or  <a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Olive" title="b1">fr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 )</div></div>
