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<b>let </b><font color="Maroon">R</font> be  non <a href="struct_0.html#V3">empty</a> <a href="waybel_0.html#V16">connected</a> <a href="orders_2.html#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font>;<br/>





<b>assume </b><a NAME="E1:63"/><i><font color="Green">E30</font></i>: 
 <a href="card_1.html#K1">Card</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1
 ;<br/>

<a NAME="E2:63"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="card_1.html#T47">CARD_1:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">a'</font> = <font color="Maroon">a</font> as  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a>  ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">w</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:63_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">w</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="bagorder.html#K11" target="_self">PosetMax</a> <font color="Maroon">a</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 ;<br/><a NAME="E2:63_1"/>
<font color="Maroon">w</font> <a href="hidden.html#R1">=</a>  <a href="bagorder.html#K11" target="_self">PosetMax</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:63_1"/>
<font color="Maroon">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="bagorder.html#T3" target="_self">Th3</a>, </i>;<br/></div><b>end;</b></div>
<a NAME="E5:63"/><b>then </b>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="bagorder.html#K11" target="_self">PosetMax</a> <font color="Maroon">a</font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E6:63"/><b>then </b><i><font color="Green">E38</font></i>: 
 <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">a'</font> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="bagorder.html#K11" target="_self">PosetMax</a> <font color="Maroon">a</font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">a'</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="bagorder.html#K11" target="_self">PosetMax</a> <font color="Maroon">a</font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="card_2.html#T63">CARD_2:63</a></i>;<br/>
<a NAME="E7:63"/>
 <a href="card_1.html#K1">Card</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="bagorder.html#K11" target="_self">PosetMax</a> <font color="Maroon">a</font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="card_1.html#T50">CARD_1:50</a></i>;<br/>
<b>hence </b><a NAME="E8:63"/>
 <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="bagorder.html#K11" target="_self">PosetMax</a> <font color="Maroon">a</font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 <b>by </b><i>, </i>;<br/>


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