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<span class="kw">let </span><font color="Maroon" title="c1">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> holds   <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">i</font> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Olive" title="b1">p</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">i</font> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span></span><br/>



<a NAME="E1:90"/><span class="lab"><font color="Green" title="E52">A1</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Maroon" title="c2">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T71" title="FINSEQ_1:th.71">FINSEQ_1:71</a></span>;<br/>
<a NAME="E2:90"/><span class="lab"><font color="Green" title="E53">A2</font></span>: 
 <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Maroon" title="c2">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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D14" title="FINSEQ_1:def.14">FINSEQ_1:def 14</a></span>;<br/>
<a NAME="E3:90"/><span class="lab"><font color="Green" title="E54">A3</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E4:90"/><span class="lab"><font color="Green" title="E55">A4</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E5:90"/>
 ex <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Olive" title="b1">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D12" title="FINSEQ_1:def.12">FINSEQ_1:def 12</a></span>;<br/>
<a NAME="E6:90"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A5</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T44" title="FINSEQ_3:th.44">FINSEQ_3:44</a></span>;<br/>
<a NAME="E7:90"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Maroon" title="c2">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T104" title="CARD_1:th.104">CARD_1:104</a></span>;<br/>
<a NAME="E8:90"/><span class="kw">then </span>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pnproc_1.html#T57" target="_self" title="PNPROC_1:th.57">Th57</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:90"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">i</font> <a href="pnproc_1.html#K12" title="PNPROC_1:func.12">Shift</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:90"><span class="lab"><font color="Green" title="E52">A1</font></span></a>, <a class="txt" href="#E2:90"><span class="lab"><font color="Green" title="E53">A2</font></span></a>, <a class="txt" href="#E3:90"><span class="lab"><font color="Green" title="E54">A3</font></span></a>, <a class="txt" href="#E4:90"><span class="lab"><font color="Green" title="E55">A4</font></span></a>, <a class="txt" href="#E6:90"><span class="lab"><font color="Green" title="E56">A5</font></span></a>, <a class="ref" href="relat_1.html#T46" title="RELAT_1:th.46">RELAT_1:46</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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