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<a NAME="E1:53"/><span class="lab"><font color="Green" title="E36">A1</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="altcat_1.html#K7" title="ALTCAT_1:func.7">EnsCat</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_1.html#D14" target="_self" title="ALTCAT_1:def.14">Def16</a>, <a class="ref" href="card_1.html#T49" title="CARD_1:th.49">CARD_1:49</a></span>;<br/>
<div><span class="kw">hereby </span> <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="altcat_1.html#D19" target="_self" title="ALTCAT_1:def.19">ALTCAT_1:def 19</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="altcat_1.html#K7" title="ALTCAT_1:func.7">EnsCat</a> 1 is 1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a> </span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c1">i</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <span class="p1">(<span class="default"><a href="altcat_1.html#K7" title="ALTCAT_1:func.7">EnsCat</a> 1</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c1">i</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> </span><br/><a NAME="E1:53_1"/>
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:53"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E2:53_1"/>
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c1">i</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_1.html#D14" target="_self" title="ALTCAT_1:def.14">Def16</a>, <a class="ref" href="altcat_1.html#T2" target="_self" title="ALTCAT_1:th.2">Th3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E3:53"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="altcat_1.html#K7" title="ALTCAT_1:func.7">EnsCat</a> 1</span>)</span> is 1 <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:53"><span class="lab"><font color="Green" title="E36">A1</font></span></a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="struct_0.html#D19" title="STRUCT_0:def.19">STRUCT_0:def 19</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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