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<a NAME="E1:27_1_1"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></span>;<br/>
<a NAME="E2:27_1_1"/>
(  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">n</font> &amp;  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="setfam_1.html#D8" title="SETFAM_1:def.8">SETFAM_1:def 8</a></span>;<br/>
<a NAME="E3:27_1_1"/><span class="kw">then </span>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="simplex0.html#K3" title="SIMPLEX0:func.3">the_subsets_with_limited_card</a> (<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Y</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27_1_1"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="simplex0.html#D2" target="_self" title="SIMPLEX0:def.2">Def2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:27_1_1"/>
 <a href="simplex0.html#K3" title="SIMPLEX0:func.3">the_subsets_with_limited_card</a> (<font color="Maroon" title="c3">n</font>,<font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Y</font>) is  <a href="simplex0.html#NV1" title="SIMPLEX0:NV.1">with_empty_element</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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