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<b>let </b><font color="Maroon" title="c1">W</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">W</font> <a href="classes1.html#NR1" title="CLASSES1:NR.1">is_Tarski-Class</a>  &amp; <font color="Maroon" title="c1">W</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies (  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">W</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">W</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">W</font> <a href="ordinal1.html#NR2" title="ORDINAL1:NR.2">is_limit_ordinal</a>  ) )</span><br/>

<b>assume </b><a NAME="E1:16"/><i><font color="Green" title="E13">A1</font></i>: 
( <font color="Maroon" title="c1">W</font> <a href="classes1.html#NR1" title="CLASSES1:NR.1">is_Tarski-Class</a>  &amp; <font color="Maroon" title="c1">W</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">W</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">W</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">W</font> <a href="ordinal1.html#NR2" title="ORDINAL1:NR.2">is_limit_ordinal</a>  )</span><br/>

<a NAME="E2:16"/><b>then </b><i><font color="Green" title="E14">A2</font></i>: 
not <font color="Maroon" title="c1">W</font>, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a> 
 
<b>by </b><i><a class="ref" href="card_1.html#T46" title="CARD_1:th.46">CARD_1:46</a></i>;<br/>
<b>hence </b><a NAME="E3:16"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">W</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="card_1.html#T21" title="CARD_1:th.21">CARD_1:21</a>, <a class="ref" href="card_1.html#T47" title="CARD_1:th.47">CARD_1:47</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">W</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">W</font> <a href="ordinal1.html#NR2" title="ORDINAL1:NR.2">is_limit_ordinal</a>  )</span><br/>

<b>thus </b><a NAME="E4:16"/>
(  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">W</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">W</font> <a href="ordinal1.html#NR2" title="ORDINAL1:NR.2">is_limit_ordinal</a>  )
 <b>by </b><i><a class="txt" href="classes2.html#E1:16"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="classes2.html#E2:16"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="classes2.html#T20" target="_self" title="CLASSES2:th.20">Th20</a>, <a class="ref" href="card_1.html#T21" title="CARD_1:th.21">CARD_1:21</a>, <a class="ref" href="card_1.html#T47" title="CARD_1:th.47">CARD_1:47</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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