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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E1:100"/>
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:100"/><span class="lab"><font color="Green" title="E49">A1</font></span>: 
<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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T43" title="CARD_1:th.43">CARD_1:43</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c2">n</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E4:100"/>
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="finseq_1.html#E13"><span class="lab"><font color="Green" title="E9">Lm1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:100"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E3:100"><span class="lab"><font color="Green" title="E49">A1</font></span></a>, <a class="ref" href="wellord2.html#T15" title="WELLORD2:th.15">WELLORD2:15</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/>


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