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

<b>let </b><font color="Maroon">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">b</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">r</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">s</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>







<b>set </b><font color="Maroon">T</font> =  <a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/>
<b>set </b><font color="Maroon">S</font> =  <a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">r</font>,<font color="Maroon">s</font>;<br/>
<b>assume </b><a NAME="E1:70"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">r</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s</font> )
 ;<br/>

<b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">r</font>,<font color="Maroon">s</font></span>)</span>;<br/>



<a NAME="E2:70"/><i><font color="Green">E38</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K1">.]</a></span> &amp; the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">r</font>,<font color="Maroon">s</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="rcomp_1.html#K1">.]</a></span> )
 
<b>by </b><i>, <a class="ref" href="topmetr.html#T25">TOPMETR:25</a></i>;<br/>
<a NAME="E3:70"/>
 <a href="jgraph_6.html#K2">closed_inside_of_rectangle</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">r</font>,<font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default">1,2 <a href="funct_4.html#K4">--&gt;</a> <span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K1">.]</a></span>,<span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="rcomp_1.html#K1">.]</a></span></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E4:70"/><b>then </b>
 <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default">1,2 <a href="funct_4.html#K4">--&gt;</a> <font color="Maroon">A</font>,<font color="Maroon">B</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="jgraph_6.html#K2">closed_inside_of_rectangle</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">r</font>,<font color="Maroon">s</font>
 
<b>by </b><i>, <a class="ref" href="topreal6.html#T29">TOPREAL6:29</a></i>;<br/>
<b>hence </b><a NAME="E5:70"/>
 <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default">1,2 <a href="funct_4.html#K4">--&gt;</a> <font color="Maroon">A</font>,<font color="Maroon">B</font></span>)</span> is   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="topreala.html#K1" target="_self">Trectangle</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">r</font>,<font color="Maroon">s</font></span>)</span>
 <b>by </b><i/>;<br/>


</div>
