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

<b>let </b><font color="Maroon">k</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">n</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">m</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">f</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">n</font>,<font color="Maroon">k</font>;<br/>







<b>assume </b><a NAME="E1:21"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<a NAME="E2:21"/>
<font color="Maroon">f</font> <a href="stirl2_1.html#K1" target="_self">"</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">m</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">n</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:21_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="stirl2_1.html#K1" target="_self">"</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">m</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<a NAME="E2:21_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#D13">FUNCT_1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E3:21_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">n</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:21"/>
 <a href="henmodel.html#K1">min*</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="stirl2_1.html#K1" target="_self">"</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">m</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i>, </i>;<br/>


</div>
