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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span>  st not <font color="Olive" title="b1">A</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a> &amp; <font color="Olive" title="b2">B</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a> holds <br/> not <font color="Olive" title="b1">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Olive" title="b2">B</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a></span><br/><b>let </b><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not <font color="Maroon" title="c2">A</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a> &amp; <font color="Maroon" title="c3">B</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a> implies  not <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c3">B</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a> )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E1:104"/><i><font color="Green" title="E50">A1</font></i>: 
not <font color="Maroon" title="c2">A</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a>
 <b>and </b><br/><a NAME="E2:104"/><i><font color="Green" title="E51">A2</font></i>: 
<font color="Maroon" title="c3">B</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c3">B</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a></span><br/>

<a NAME="E3:104"/><i><font color="Green" title="E52">A3</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">B</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a>
 
<b>by </b><i><a class="txt" href="topreal6.html#E2:104"><i><font color="Green" title="E51">A2</font></i></a>, <a class="ref" href="topreal6.html#T98" target="_self" title="TOPREAL6:th.98">Th98</a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">B</font></span>)</span> = 
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c3">B</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T52" title="XBOOLE_1:th.52">XBOOLE_1:52</a></i>
<br/>.= 
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="ref" href="xboole_1.html#T37" title="XBOOLE_1:th.37">XBOOLE_1:37</a></i>
<br/>.= 
<font color="Maroon" title="c2">A</font>

;<br/>
<b>hence </b><a NAME="E5:104"/>
not <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c3">B</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a>
 <b>by </b><i><a class="txt" href="topreal6.html#E1:104"><i><font color="Green" title="E50">A1</font></i></a>, <a class="txt" href="topreal6.html#E3:104"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="topreal6.html#T76" target="_self" title="TOPREAL6:th.76">Th76</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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