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<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><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="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">i</font>, <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">j</font>;<br/>









<b>assume </b><a NAME="E1:48"/><i><font color="Green">E45</font></i>: 
( ( <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> 0 implies <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0 ) &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font> )
 ;<br/>

<b>set </b><font color="Maroon">q</font> = <font color="Maroon">p</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font>;<br/>
<a NAME="E2:48"/>
(  <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a>, <a class="ref" href="relat_1.html#T45">RELAT_1:45</a></i>;<br/>
<a NAME="E3:48"/><b>then </b>
( <font color="Maroon">p</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font> is   <a href="finseq_1.html#NM1">FinSequence</a> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font> )
 
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E4:48"/>
<font color="Maroon">p</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font> is    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>


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