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<span class="kw">let </span><font color="Maroon" title="c1">M</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">M</font> is  <a href="card_1.html#V1" title="CARD_1:attr.1">cardinal</a>  implies <font color="Maroon" title="c1">M</font> is  <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:5_1_1"/>
<font color="Maroon" title="c1">M</font> is  <a href="card_1.html#V1" title="CARD_1:attr.1">cardinal</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">M</font> is  <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a> </span><br/>

<a NAME="E2:5_1_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">B</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> st <br/>( <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">B</font> &amp; ( for <font color="Olive" title="b2">A</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>  st <font color="Olive" title="b2">A</font>,<font color="Olive" title="b1">B</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  holds <br/><font color="Olive" title="b1">B</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b2">A</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D1" target="_self" title="CARD_1:def.1">Def1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:5_1_1"/>
<font color="Maroon" title="c1">M</font> is  <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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