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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 ( <font color="Olive" title="b1">A</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a> or <font color="Olive" title="b2">B</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a> ) holds <br/><font color="Olive" title="b1">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</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"> ( ( <font color="Maroon" title="c2">A</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a> or <font color="Maroon" title="c3">B</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a> ) implies <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> )</span><br/>



<b>assume </b><a NAME="E1:103"/><i><font color="Green" title="E50">A1</font></i>: 
( <font color="Maroon" title="c2">A</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a> or <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"> <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></span><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" title="c2">A</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a> or <font color="Maroon" title="c3">B</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a> )
 </span><b>by </b><i><a class="txt" href="topreal6.html#E1:103"><i><font color="Green" title="E50">A1</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"/>
<font color="Maroon" title="c2">A</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"> <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></span><br/><div class="add"><b>hence </b><a NAME="E2:103_1_1"/>
<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="ref" href="jordan2c.html#T16" title="JORDAN2C:th.16">JORDAN2C:16</a>, <a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><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"/>
<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"> <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></span><br/><div class="add"><b>hence </b><a NAME="E2:103_1_2"/>
<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="ref" href="jordan2c.html#T16" title="JORDAN2C:th.16">JORDAN2C:16</a>, <a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

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