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<b>let </b><font color="Maroon">p</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:95"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">p</font> is <a href="funct_1.html#V2">one-to-one</a>
 ;<br/>

<a NAME="E2:95"/><i><font color="Green">E42</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E3:95"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/>
<a NAME="E4:95"/><b>then </b>
( <font color="Maroon">p</font> <a href="finseq_3.html#K1" target="_self">-</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K14">Sgm</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">A</font></span>)</span></span>)</span> is <a href="funct_1.html#V2">one-to-one</a> )
 
<b>by </b><i><a class="txt" href="finseq_3.html#E44"><i><font color="Green">Lemma63</font></i></a>, </i>;<br/>
<b>hence </b><a NAME="E5:95"/>
<font color="Maroon">p</font> <a href="finseq_3.html#K1" target="_self">-</a> <font color="Maroon">A</font> is <a href="funct_1.html#V2">one-to-one</a>
 <b>by </b><i><a class="ref" href="finseq_3.html#T43" target="_self">Th43</a>, <a class="ref" href="funct_1.html#T46">FUNCT_1:46</a></i>;<br/>


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