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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:73"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>and </b><br/><a NAME="E2:73"/><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="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>assume </b><a NAME="E3:73"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="jordan2c.html#V1">Bounded</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> as  <a href="tbsp_1.html#V6">bounded</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14">Euclid</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="jordan2c.html#D2">JORDAN2C:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14">Euclid</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="topreal3.html#T13">TOPREAL3:13</a></i>;<br/>
<a NAME="E6:73"/><i><font color="Green">E39</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14">Euclid</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="topreal6.html#E2:73"><i><font color="Green">E38</font></i></a>, <a class="ref" href="topreal3.html#T13">TOPREAL3:13</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> =  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14">Euclid</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="topreal3.html#T13">TOPREAL3:13</a></i>;<br/>
<i><font color="Green">E40</font></i>: <font color="Maroon">c<sub>7</sub></font> = 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>

<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14">Euclid</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="topreal3.html#T13">TOPREAL3:13</a></i>
<br/>.= 
 <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="euclid.html#K14">Euclid</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>

;<br/>
<a NAME="E9:73"/>
not  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> is <a href="jordan2c.html#V1">Bounded</a>
 
<b>by </b><i><a class="txt" href="topreal6.html#E1:73"><i><font color="Green">E37</font></i></a>, <a class="ref" href="jordan2c.html#T41">JORDAN2C:41</a></i>;<br/>
<a NAME="E10:73"/><b>then </b>
not <font color="Maroon">c<sub>7</sub></font> is <a href="tbsp_1.html#V6">bounded</a>
 
<b>by </b><i><a class="ref" href="jordan2c.html#D2">JORDAN2C:def 2</a></i>;<br/>
<a NAME="E11:73"/><b>then </b>
not  <a href="euclid.html#K14">Euclid</a> <font color="Maroon">c<sub>1</sub></font> is <a href="tbsp_1.html#V5">bounded</a>
 
<b>by </b><i><a class="txt" href="topreal6.html#E8:73"><i><font color="Green">E40</font></i></a>, <a class="ref" href="tbsp_1.html#T25">TBSP_1:25</a></i>;<br/>
<a NAME="E12:73"/><b>then </b>
not <font color="Maroon">c<sub>6</sub></font> is <a href="tbsp_1.html#V6">bounded</a>
 
<b>by </b><i><a class="txt" href="topreal6.html#E6:73"><i><font color="Green">E39</font></i></a>, <a class="ref" href="topreal6.html#T73" target="_self">Th73</a></i>;<br/>
<b>hence </b><a NAME="E13:73"/>
not <font color="Maroon">c<sub>4</sub></font> is <a href="jordan2c.html#V1">Bounded</a>
 <b>by </b><i><a class="ref" href="jordan2c.html#D2">JORDAN2C:def 2</a></i>;<br/>


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