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<a NAME="E1:57"/><i><font color="Green">E15</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="altcat_1.html#K7" target="_self">EnsCat</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="card_5.html#T1">CARD_5:1</a></i>;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_1.html#D21" target="_self">ALTCAT_1:def 21</a>
<div class="add"><b>let </b><font color="Maroon">i</font> be   <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><a href="altcat_1.html#K7" target="_self">EnsCat</a> 1</span>)</span>;<br/><a NAME="E1:57_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E2:57_1"/>
<span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">i</font>,<font color="Maroon">i</font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span> is <a href="realset1.html#V1">trivial</a>
 <b>by </b><i>, </i>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">o1</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="altcat_1.html#K7" target="_self">EnsCat</a> 1</span>)</span>, <font color="Maroon">o2</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="altcat_1.html#K7" target="_self">EnsCat</a> 1</span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="realset2.html#D7">REALSET2:def 7</a><br/>

<a NAME="E3:57"/>
( <font color="Maroon">o1</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">o2</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:57"/>
<font color="Maroon">o1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o2</font>
 ;<br/>


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