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<b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">f</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:57"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E2:57"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E3:57"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">x</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font>
 ;<br/>

<b>set </b><font color="Maroon">g</font> = <font color="Maroon">f</font> <a href="finseq_5.html#K1" target="_self">-:</a> <font color="Maroon">p</font>;<br/>
<b>set </b><font color="Maroon">i</font> = <font color="Maroon">x</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font>;<br/>
<a NAME="E4:57"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">x</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="finseq_4.html#T30">FINSEQ_4:30</a></i>;<br/>
<a NAME="E5:57"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">x</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="finseq_4.html#T31">FINSEQ_4:31</a></i>;<br/>
<a NAME="E6:57"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">x</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E7:57"/>
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="finseq_5.html#K1" target="_self">-:</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_5.html#K1" target="_self">-:</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="E8:57"/><b>then </b><i><font color="Green">E36</font></i>: 
<font color="Maroon">x</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_5.html#K1" target="_self">-:</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i><a class="txt" href="finseq_5.html#E4:57"><i><font color="Green">E32</font></i></a>, , </i>;<br/>
<a NAME="E9:57"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_5.html#K1" target="_self">-:</a> <font color="Maroon">p</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_5.html#K1" target="_self">-:</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E10:57"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_5.html#K1" target="_self">-:</a> <font color="Maroon">p</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_5.html#K1" target="_self">-:</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i><a class="txt" href="finseq_5.html#E8:57"><i><font color="Green">E36</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<a NAME="E11:57"/><b>then </b>
<font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_5.html#K1" target="_self">-:</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i><a class="txt" href="finseq_5.html#E4:57"><i><font color="Green">E32</font></i></a>, , </i>;<br/>
<a NAME="E12:57"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_5.html#K1" target="_self">-:</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i><a class="txt" href="finseq_5.html#E6:57"><i><font color="Green">E34</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<b>hence </b><a NAME="E13:57"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_5.html#K1" target="_self">-:</a> <font color="Maroon">p</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_4.html#T29">FINSEQ_4:29</a></i>;<br/>


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