<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E36">Th34</font></span>: <a NAME="T42"><span class="comment"><font color="firebrick">:: SRINGS_5:42</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="srings_4.html#NK4" title="SRINGS_4:NK.4">MeasurableRectangle</a> <span class="p1">(<span class="default"><a href="srings_5.html#K14" title="SRINGS_5:func.14">ProductRightOpenIntervals</a> <font color="Olive" title="b1">n</font></span>)</span> holds <br/> ex <font color="Olive" title="b3">y</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Olive" title="b1">n</font></span>)</span> ex <font color="Olive" title="b4">f</font> being  <font color="Olive">b<sub>1</sub></font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> st <br/>( <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">y</font> &amp; (  for <font color="Olive" title="b5">t</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Olive" title="b1">n</font> holds <br/> ( <font color="Olive" title="b5">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">y</font> iff  for <font color="Olive" title="b6">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b6">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Olive" title="b1">n</font> holds <br/><font color="Olive" title="b5">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">[.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b6">i</font></span>)</span> <a href="srings_5.html#K2" title="SRINGS_5:func.2">`1</a></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b6">i</font></span>)</span> <a href="srings_5.html#K3" title="SRINGS_5:func.3">`2</a></span>)</span></span><a href="rcomp_1.html#K3" title="RCOMP_1:func.3">.[</a></span> ) ) )</div></div>
