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<b>let </b><font color="Maroon" title="c1">X</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">X</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> implies  ex <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <font color="Maroon" title="c1">X</font>, <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Olive" title="b1">n</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  )</span><br/>

<b>assume </b><a NAME="E1:98"/>
<font color="Maroon" title="c1">X</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <font color="Maroon" title="c1">X</font>, <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Olive" title="b1">n</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a> </span><br/>

<b>then consider </b><font color="Maroon" title="c2">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E3:98"/><i><font color="Green" title="E50">A1</font></i>: 
<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">n</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a> 
 <b>by </b><i><a class="ref" href="card_1.html#T74" title="CARD_1:th.74">CARD_1:74</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c2">n</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">X</font>, <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">n</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a> </span><br/>

<a NAME="E4:98"/>
<font color="Maroon" title="c2">n</font>, <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">n</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a> 
 
<b>by </b><i><a class="txt" href="finseq_1.html#E15"><i><font color="Green" title="E9">Lm1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:98"/>
<font color="Maroon" title="c1">X</font>, <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">n</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a> 
 <b>by </b><i><a class="txt" href="finseq_1.html#E3:98"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="wellord2.html#T22" title="WELLORD2:th.22">WELLORD2:22</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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