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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">p</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>



<a NAME="E1:91"/><i><font color="Green">E29</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T71">FINSEQ_1:71</a></i>;<br/>
<a NAME="E2:91"/><i><font color="Green">E30</font></i>: 
 <a href="finseq_1.html#K15">Seq</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">p</font></span>)</span> <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"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D14">FINSEQ_1:def 14</a></i>;<br/>
<a NAME="E3:91"/><i><font color="Green">E35</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> &amp;  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <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> <span class="p2">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<b>consider </b><font color="Maroon">k</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E5:91"/><i><font color="Green">E37</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D12">FINSEQ_1:def 12</a></i>;<br/>
<a NAME="E6:91"/><i><font color="Green">E38</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">p</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="finseq_3.html#T44">FINSEQ_3:44</a></i>;<br/>
<a NAME="E7:91"/>
 <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pre_circ.html#T21">PRE_CIRC:21</a></i>;<br/>
<a NAME="E8:91"/><b>then </b>
 <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T9" target="_self">Th9</a></i>;<br/>
<b>hence </b><a NAME="E9:91"/>
 <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> <span class="p1">(<span class="default"><a href="finseq_1.html#K15">Seq</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="pnproc_1.html#K14" target="_self">Shift</a> <font color="Maroon">p</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="pnproc_1.html#E14"><i><font color="Green">Lemma58</font></i></a>, <a class="ref" href="pnproc_1.html#T10" target="_self">Th10</a>, , , <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/>


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