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<b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">D</font>;<br/>



<b>thus </b><a NAME="E1:10"/>
( <font color="Maroon">A</font> is <a href="rearran1.html#V3" target="_self">lenght_equal_card_of_set</a> implies  <a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">D</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:10_1"/>
<font color="Maroon">A</font> is <a href="rearran1.html#V3" target="_self">lenght_equal_card_of_set</a>
 ;<br/>

<b>then consider </b><font color="Maroon">B</font> being  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:10_1"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">D</font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">B</font> )
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E4:10_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">D</font>
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T99">ZFMISC_1:99</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:10"/><i><font color="Green">E34</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">D</font>
 ;<br/>

<b>take </b>
<font color="Maroon">D</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="rearran1.html#D3" target="_self">REARRAN1:def 3</a><br/>

<b>thus </b><a NAME="E3:10"/>
( <font color="Maroon">D</font> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">D</font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">D</font> )
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T99">ZFMISC_1:99</a></i>;<br/>


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