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<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>let </b><font color="Maroon">F</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>





<b>assume </b><a NAME="E1:74"/><i><font color="Green">E45</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font>
 ;<br/>

<b>set </b><font color="Maroon">q</font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font>;<br/>
<a NAME="E2:74"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E3:74"/><b>then </b>
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">p</font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="funct_3.html#T71">FUNCT_3:71</a>, <a class="ref" href="zfmisc_1.html#T118">ZFMISC_1:118</a></i>;<br/>
<a NAME="E4:74"/><b>then </b>
(  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">p</font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E5:74"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">p</font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> &amp; <font color="Maroon">F</font> <a href="funcop_1.html#K5">[;]</a> <font color="Maroon">a</font>,<font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">p</font></span><a href="funct_3.html#K13">:&gt;</a></span> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">p</font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font> )
 
<b>by </b><i><a class="ref" href="finseq_2.html#T16" target="_self">Th16</a>, <a class="ref" href="funcop_1.html#D5">FUNCOP_1:def 5</a>, <a class="ref" href="funct_3.html#T70">FUNCT_3:70</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E6:74"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funcop_1.html#K5">[;]</a> <font color="Maroon">a</font>,<font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/>


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