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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<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="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>, <font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>;<br/>



<b>assume </b><a NAME="E1:103"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">A</font> is <a href="jordan2c.html#V1">Bounded</a> or <font color="Maroon">B</font> is <a href="jordan2c.html#V1">Bounded</a> )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:103_1"/>
( <font color="Maroon">A</font> is <a href="jordan2c.html#V1">Bounded</a> or <font color="Maroon">B</font> is <a href="jordan2c.html#V1">Bounded</a> )
 </span><b>by </b><i><a class="txt" href="topreal6.html#E1"><i><font color="Green">Lemma54</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_1"><b>suppose </b></a><a NAME="E1:103_1_1"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">A</font> is <a href="jordan2c.html#V1">Bounded</a>
 ;<br/><div class="add"><a NAME="E2:103_1_1"/>
<font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E3:103_1_1"/>
<font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font> is <a href="jordan2c.html#V1">Bounded</a>
 <b>by </b><i><a class="ref" href="topreal6.html#T6" target="_self">Th6</a>, <a class="ref" href="jordan2c.html#T16">JORDAN2C:16</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_2"><b>suppose </b></a><a NAME="E1:103_1_2"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">B</font> is <a href="jordan2c.html#V1">Bounded</a>
 ;<br/><div class="add"><a NAME="E2:103_1_2"/>
<font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E3:103_1_2"/>
<font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font> is <a href="jordan2c.html#V1">Bounded</a>
 <b>by </b><i><a class="ref" href="topreal6.html#T6" target="_self">Th6</a>, <a class="ref" href="jordan2c.html#T16">JORDAN2C:16</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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