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

<b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">r</font>, <font color="Maroon" title="c6">s</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>







<b>set </b><font color="Maroon" title="c7">A</font> = <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c8">B</font> = <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c5">r</font>,<font color="Maroon" title="c6">s</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c9">f</font> = 1,2 <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c5">r</font>,<font color="Maroon" title="c6">s</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c10">R</font> =  <a href="jgraph_6.html#K2" title="JGRAPH_6:func.2">closed_inside_of_rectangle</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">r</font>,<font color="Maroon" title="c6">s</font>;<br/>
<a NAME="E1:45"/><i><font color="Green" title="E17">A1</font></i>: 
 <a href="jgraph_6.html#K2" title="JGRAPH_6:func.2">closed_inside_of_rectangle</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">r</font>,<font color="Maroon" title="c6">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">p</font> where <font color="Olive" title="b1">p</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> : ( <font color="Maroon" title="c3">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  &amp; <font color="Olive" title="b1">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c5">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  &amp; <font color="Olive" title="b1">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">s</font> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="jgraph_6.html#D2" title="JGRAPH_6:def.2">JGRAPH_6:def 2</a></i>;<br/>
<b>thus </b><a NAME="E2:45"/>
 <a href="jgraph_6.html#K2" title="JGRAPH_6:func.2">closed_inside_of_rectangle</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">r</font>,<font color="Maroon" title="c6">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default">1,2 <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c5">r</font>,<font color="Maroon" title="c6">s</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c11">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:45_1"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jgraph_6.html#K2" title="JGRAPH_6:func.2">closed_inside_of_rectangle</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">r</font>,<font color="Maroon" title="c6">s</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c12">p</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span><b> such that </b><br/><a NAME="E3:45_1"/><i><font color="Green" title="E18">A2</font></i>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">p</font>
 <b>and </b><br/><a NAME="E4:45_1"/><i><font color="Green" title="E19">A3</font></i>: 
( <font color="Maroon" title="c3">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  &amp; <font color="Maroon" title="c12">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c5">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  &amp; <font color="Maroon" title="c12">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">s</font> )
 <b>by </b><i><a class="txt" href="topreala.html#E1:45"><i><font color="Green" title="E17">A1</font></i></a></i>;<br/>
<a NAME="E5:45_1"/><i><font color="Green" title="E20">A4</font></i>: 
( <font color="Maroon" title="c12">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> &amp; <font color="Maroon" title="c12">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c5">r</font>,<font color="Maroon" title="c6">s</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> )
 
<b>by </b><i><a class="txt" href="topreala.html#E4:45_1"><i><font color="Green" title="E19">A3</font></i></a></i>;<br/>
<a NAME="E6:45_1"/>
<span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1,2 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="topreala.html#T49" target="_self" title="TOPREALA:th.49">Th49</a></i>;<br/>
<a NAME="E7:45_1"/><b>then </b>
<font color="Maroon" title="c12">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1,2 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="euclid.html#T57" title="EUCLID:th.57">EUCLID:57</a></i>;<br/>
<b>hence </b><a NAME="E8:45_1"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default">1,2 <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c5">r</font>,<font color="Maroon" title="c6">s</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="topreala.html#E3:45_1"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="topreala.html#E5:45_1"><i><font color="Green" title="E20">A4</font></i></a>, <a class="ref" href="hilbert3.html#T11" title="HILBERT3:th.11">HILBERT3:11</a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c11">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E3:45"/><i><font color="Green" title="E18">A5</font></i>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default">1,2 <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c5">r</font>,<font color="Maroon" title="c6">s</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c12">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E5:45"/><i><font color="Green" title="E19">A6</font></i>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">g</font>
 <b>and </b><br/><a NAME="E6:45"/><i><font color="Green" title="E20">A7</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c12">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">1,2 <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c5">r</font>,<font color="Maroon" title="c6">s</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span>
 <b>and </b><br/><a NAME="E7:45"/>
for <font color="Olive" title="b1">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">1,2 <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c5">r</font>,<font color="Maroon" title="c6">s</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> holds <br/><font color="Maroon" title="c12">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default">1,2 <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c5">r</font>,<font color="Maroon" title="c6">s</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">y</font>
 <b>by </b><i><a class="ref" href="card_3.html#D5" title="CARD_3:def.5">CARD_3:def 5</a></i>;<br/>
<a NAME="E8:45"/><i><font color="Green" title="E21">A8</font></i>: 
( <font color="Maroon" title="c12">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> &amp; <font color="Maroon" title="c12">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c5">r</font>,<font color="Maroon" title="c6">s</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> )
 
<b>by </b><i><a class="txt" href="topreala.html#E3:45"><i><font color="Green" title="E18">A5</font></i></a>, <a class="txt" href="topreala.html#E5:45"><i><font color="Green" title="E19">A6</font></i></a>, <a class="ref" href="topreala.html#T24" target="_self" title="TOPREALA:th.24">Th24</a></i>;<br/>
<a NAME="E9:45"/><i><font color="Green" title="E22">A9</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">1,2 <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c5">r</font>,<font color="Maroon" title="c6">s</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c13">g1</font> = <font color="Maroon" title="c12">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1, <font color="Maroon" title="c14">g2</font> = <font color="Maroon" title="c12">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> <b>by </b><i><a class="txt" href="topreala.html#E8:45"><i><font color="Green" title="E21">A8</font></i></a></i>;<br/>
<a NAME="E11:45"/><i><font color="Green" title="E23">A10</font></i>: 
<span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><font color="Maroon" title="c13">g1</font>,<font color="Maroon" title="c14">g2</font></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1,2 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c13">g1</font>,<font color="Maroon" title="c14">g2</font>
 
<b>by </b><i><a class="ref" href="topreala.html#T49" target="_self" title="TOPREALA:th.49">Th49</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c15">g</font> = <font color="Maroon" title="c12">g</font> as   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> <b>by </b><i><a class="txt" href="topreala.html#E6:45"><i><font color="Green" title="E20">A7</font></i></a>, <a class="txt" href="topreala.html#E9:45"><i><font color="Green" title="E22">A9</font></i></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="finseq_1.html#D2" title="FINSEQ_1:def.2">FINSEQ_1:def 2</a></i>;<br/>
<a NAME="E13:45"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<b>by </b><i><a class="txt" href="topreala.html#E6:45"><i><font color="Green" title="E20">A7</font></i></a>, <a class="txt" href="topreala.html#E9:45"><i><font color="Green" title="E22">A9</font></i></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c16">g</font> = <font color="Maroon" title="c15">g</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <b>by </b><i><a class="txt" href="topreala.html#E11:45"><i><font color="Green" title="E23">A10</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>;<br/>
<a NAME="E15:45"/>
( <font color="Maroon" title="c3">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c16">g</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  &amp; <font color="Maroon" title="c16">g</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c5">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c16">g</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  &amp; <font color="Maroon" title="c16">g</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">s</font> )
 
<b>by </b><i><a class="txt" href="topreala.html#E8:45"><i><font color="Green" title="E21">A8</font></i></a>, <a class="ref" href="rcomp_1.html#T48" title="RCOMP_1:th.48">RCOMP_1:48</a></i>;<br/>
<b>hence </b><a NAME="E16:45"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="jgraph_6.html#K2" title="JGRAPH_6:func.2">closed_inside_of_rectangle</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">r</font>,<font color="Maroon" title="c6">s</font>
 <b>by </b><i><a class="txt" href="topreala.html#E1:45"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="topreala.html#E5:45"><i><font color="Green" title="E19">A6</font></i></a></i>;<br/>


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