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

<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="compts_1.html#V6">compact</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>, <font color="Maroon">Y</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="compts_1.html#V6">compact</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:17"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font>
 <b>and </b><br/><a NAME="E2:17"/><i><font color="Green">E39</font></i>: 
 <a href="pscomp_1.html#K30">N-max</a> <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E3:17"/><i><font color="Green">E40</font></i>: 
 <a href="pscomp_1.html#K16">N-bound</a> <font color="Maroon">X</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="pscomp_1.html#K16">N-bound</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="pscomp_1.html#T129">PSCOMP_1:129</a></i>;<br/>
<a NAME="E4:17"/><i><font color="Green">E41</font></i>: 
( <span class="p1">(<span class="default"><a href="pscomp_1.html#K30">N-max</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K16">N-bound</a> <font color="Maroon">X</font> &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K30">N-max</a> <font color="Maroon">Y</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K16">N-bound</a> <font color="Maroon">Y</font> )
 
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E5:17"/>
 <a href="pscomp_1.html#K16">N-bound</a> <font color="Maroon">X</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K30">N-max</a> <font color="Maroon">Y</font></span>)</span> <a href="euclid.html#K22">`2</a> 
 
<b>by </b><i>, <a class="ref" href="pscomp_1.html#T71">PSCOMP_1:71</a></i>;<br/>
<a NAME="E6:17"/><b>then </b><i><font color="Green">E42</font></i>: 
 <a href="pscomp_1.html#K16">N-bound</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K16">N-bound</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, , <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>
<a NAME="E7:17"/><b>then </b>
 <a href="pscomp_1.html#K30">N-max</a> <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K24">N-most</a> <font color="Maroon">X</font>
 
<b>by </b><i>, , <a class="ref" href="sprect_2.html#T14">SPRECT_2:14</a></i>;<br/>
<a NAME="E8:17"/><b>then </b><i><font color="Green">E43</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K30">N-max</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K30">N-max</a> <font color="Maroon">Y</font></span>)</span> <a href="euclid.html#K21">`1</a> 
 
<b>by </b><i><a class="ref" href="pscomp_1.html#T98">PSCOMP_1:98</a></i>;<br/>
<a NAME="E9:17"/>
 <a href="pscomp_1.html#K30">N-max</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="sprect_1.html#T13">SPRECT_1:13</a></i>;<br/>
<a NAME="E10:17"/><b>then </b>
 <a href="pscomp_1.html#K30">N-max</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K24">N-most</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, , , <a class="ref" href="sprect_2.html#T14">SPRECT_2:14</a></i>;<br/>
<a NAME="E11:17"/><b>then </b>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K30">N-max</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K30">N-max</a> <font color="Maroon">Y</font></span>)</span> <a href="euclid.html#K21">`1</a> 
 
<b>by </b><i><a class="ref" href="pscomp_1.html#T98">PSCOMP_1:98</a></i>;<br/>
<a NAME="E12:17"/><b>then </b>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K30">N-max</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K30">N-max</a> <font color="Maroon">Y</font></span>)</span> <a href="euclid.html#K21">`1</a> 
 
<b>by </b><i>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>
<b>hence </b><a NAME="E13:17"/>
 <a href="pscomp_1.html#K30">N-max</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K30">N-max</a> <font color="Maroon">Y</font>
 <b>by </b><i>, , <a class="ref" href="topreal3.html#T11">TOPREAL3:11</a></i>;<br/>


</div>
