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<b>let </b><font color="Maroon" title="c1">k</font>, <font color="Maroon" title="c2">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c3">p</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>;<br/>





<b>assume </b><a NAME="E1:93"/><i><font color="Green" title="E60">A1</font></i>: 
<font color="Maroon" title="c1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">p</font>
 ;<br/>

<a NAME="E2:93"/><b>then </b><i><font color="Green" title="E61">A2</font></i>: 
<font color="Maroon" title="c1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="pnproc_1.html#K14" title="PNPROC_1:func.14">Shift</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="pnproc_1.html#T58" target="_self" title="PNPROC_1:th.58">Th58</a></i>;<br/>
<a NAME="E3:93"/><i><font color="Green" title="E62">A3</font></i>: 
 <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="pnproc_1.html#K14" title="PNPROC_1:func.14">Shift</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="pnproc_1.html#K14" title="PNPROC_1:func.14">Shift</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="pnproc_1.html#K14" title="PNPROC_1:func.14">Shift</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D14" title="FINSEQ_1:def.14">FINSEQ_1:def 14</a></i>;<br/>
<a NAME="E4:93"/><i><font color="Green" title="E63">A4</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="pnproc_1.html#K14" title="PNPROC_1:func.14">Shift</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="pnproc_1.html#K14" title="PNPROC_1:func.14">Shift</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="pnproc_1.html#K14" title="PNPROC_1:func.14">Shift</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">k</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D14" title="FINSEQ_1:def.14">FINSEQ_1:def 14</a></i>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="pnproc_1.html#K14" title="PNPROC_1:func.14">Shift</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="pnproc_1.html#K14" title="PNPROC_1:func.14">Shift</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">k</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="pnproc_1.html#K14" title="PNPROC_1:func.14">Shift</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="pnproc_1.html#K14" title="PNPROC_1:func.14">Shift</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">k</font></span>)</span>
<b>by </b><i><a class="txt" href="pnproc_1.html#E2:93"><i><font color="Green" title="E61">A2</font></i></a>, <a class="txt" href="pnproc_1.html#E3:93"><i><font color="Green" title="E62">A3</font></i></a>, <a class="ref" href="funct_1.html#T22" title="FUNCT_1:th.22">FUNCT_1:22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="pnproc_1.html#K14" title="PNPROC_1:func.14">Shift</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>
<b>by </b><i><a class="txt" href="pnproc_1.html#E1:93"><i><font color="Green" title="E60">A1</font></i></a>, <a class="ref" href="pnproc_1.html#T59" target="_self" title="PNPROC_1:th.59">Th59</a></i>
;<br/>
<b>hence </b><a NAME="E6:93"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="pnproc_1.html#K14" title="PNPROC_1:func.14">Shift</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">k</font>
 <b>by </b><i><a class="txt" href="pnproc_1.html#E1:93"><i><font color="Green" title="E60">A1</font></i></a>, <a class="txt" href="pnproc_1.html#E4:93"><i><font color="Green" title="E63">A4</font></i></a>, <a class="ref" href="pnproc_1.html#D15" target="_self" title="PNPROC_1:def.15">Def15</a></i>;<br/>


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