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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>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</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>thus </b><a NAME="E1:58"/>
<font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K6" target="_self">(o)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">c<sub>3</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:58_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K6" target="_self">(o)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">c<sub>3</sub></font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:58_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K6" target="_self">(o)</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="mathmorp.html#T41" target="_self">Th41</a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K6" target="_self">(o)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="mathmorp.html#T9" target="_self">Th9</a></i>;<br/>


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

<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K6" target="_self">(o)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="mathmorp.html#K3" target="_self">(-)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">c<sub>3</sub></font>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="mathmorp.html#K5" target="_self">(O)</a> <font color="Maroon">c<sub>3</sub></font>

;<br/>
<b>hence </b><a NAME="E3:58_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K6" target="_self">(o)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="mathmorp.html#T41" target="_self">Th41</a></i>;<br/>


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

<b>thus </b><a NAME="E2:58"/>
<font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K3" target="_self">(-)</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K5" target="_self">(O)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="mathmorp.html#K3" target="_self">(-)</a> <font color="Maroon">c<sub>3</sub></font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_2"><b>proof </b></a><div class="add">

<a NAME="E1:58_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K5" target="_self">(O)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="mathmorp.html#K3" target="_self">(-)</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K3" target="_self">(-)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="mathmorp.html#K6" target="_self">(o)</a> <font color="Maroon">c<sub>3</sub></font>
 
;<br/>
<b>hence </b><a NAME="E2:58_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K3" target="_self">(-)</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K5" target="_self">(O)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="mathmorp.html#K3" target="_self">(-)</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="mathmorp.html#T41" target="_self">Th41</a></i>;<br/>


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

<a NAME="E3:58"/>
<font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K5" target="_self">(O)</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="mathmorp.html#T41" target="_self">Th41</a></i>;<br/>
<b>hence </b><a NAME="E4:58"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K5" target="_self">(O)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="mathmorp.html#K3" target="_self">(-)</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K3" target="_self">(-)</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="mathmorp.html#T9" target="_self">Th9</a></i>;<br/>


</div>
