<?xml version="1.0"?>
<div class="add">

<a NAME="E1:31_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="finseq_3.html#T29" onmouseover="rs('finseq_3/T29')" onmouseout="rh()">FINSEQ_3:29</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">z</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><span class="kw"> such that </span><br/><a NAME="E3:31_1_1"/><span class="lab"><font color="Green" title="E27">A2</font></span>: 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">z</font>
 <span class="kw">and </span><br/><a NAME="E4:31_1_1"/><span class="lab"><font color="Green" title="E28">A3</font></span>: 
( <font color="Maroon" title="c3">z</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Maroon" title="c2">m</font> &amp; (  for <font color="Olive" title="b1">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">i</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="Maroon" title="c1">u</font> holds <br/><font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c1">u</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Maroon" title="c2">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_6.html#T41" onmouseover="rs('int_6/T41')" onmouseout="rh()">INT_6:41</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">z</font> = <font color="Maroon" title="c3">z</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:31_1_1"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="ref" href="int_1.html#T3" onmouseover="rs('int_1/T3')" onmouseout="rh()">INT_1:3</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">z</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">z</font> <a href="number14.html#R2" title="NUMBER14:pred.2">solves_CRT</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c2">m</font> &amp; <font color="Maroon" title="c4">z</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Maroon" title="c2">m</font> )</span><br/>

<span class="kw">thus </span><a NAME="E6:31_1_1"/>
( <font color="Maroon" title="c4">z</font> <a href="number14.html#R2" title="NUMBER14:pred.2">solves_CRT</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c2">m</font> &amp; <font color="Maroon" title="c4">z</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Maroon" title="c2">m</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:31_1_1"><span class="lab"><font color="Green" title="E28">A3</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
