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<div class="add">

<b>let </b><font color="Maroon" title="c1">D</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">f</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ;<br/><b>let </b><font color="Maroon" title="c3">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>





<a NAME="E1:31"/><i><font color="Green" title="E21">A1</font></i>: 
( <span class="p1">(<span class="default"><a href="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c3">i</font></span>)</span> &amp; <font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c3">i</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D15" title="FINSEQ_1:def.15">FINSEQ_1:def 15</a></i>;<br/>
<a NAME="E2:31"/><i><font color="Green" title="E22">A2</font></i>: 
 <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <font color="Maroon" title="c2">f</font>
 
<b>by </b><i><a class="ref" href="card_3.html#D2" title="CARD_3:def.2">CARD_3:def 2</a></i>;<br/>
<a NAME="E3:31"/>
 <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font></span>)</span>
 
<b>by </b><i><a class="ref" href="card_3.html#D2" title="CARD_3:def.2">CARD_3:def 2</a></i>;<br/>
<b>then </b><i><font color="Green" title="E23">A3</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>
<br/>.= 
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E1:31"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="finseq_2.html#T24" title="FINSEQ_2:th.24">FINSEQ_2:24</a></i>
;<br/>
<b>reconsider </b><font color="Maroon" title="c4">k</font> =  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font></span>)</span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T1" title="FINSEQ_2:th.1">FINSEQ_2:1</a></i>;<br/>
<i><font color="Green" title="E24">A4</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font></span>)</span> = 
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c3">i</font>,<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="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E1:31"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="finseq_2.html#T24" title="FINSEQ_2:th.24">FINSEQ_2:24</a></i>
<br/>.= 
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E2:31"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">j</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:31_3"/><i><font color="Green" title="E25">A5</font></i>: 
<font color="Maroon" title="c5">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c4">k</font>
 ;<br/><a NAME="E2:31_3"/><i><font color="Green" title="E26">A6</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <font color="Maroon" title="c2">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom3.html#E2:31"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:31_3_1"/>
( <font color="Maroon" title="c3">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font> or <font color="Maroon" title="c3">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_3_1_1"><b>suppose </b></a><a NAME="E1:31_3_1_1"/><i><font color="Green" title="E27">A7</font></i>: 
<font color="Maroon" title="c3">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font>
 ;<br/><div class="add"><a NAME="E2:31_3_1_1"/><b>then </b><i><font color="Green" title="E28">A8</font></i>: 
<font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i</font>
 <b>by </b><i><a class="ref" href="xxreal_0.html#D8" title="XXREAL_0:def.8">XXREAL_0:def 8</a></i>;<br/><a NAME="E3:31_3_1_1"/><i><font color="Green" title="E29">A9</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i</font>
 <b>by </b><i><a class="txt" href="polynom3.html#E1:31_3_1_1"><i><font color="Green" title="E27">A7</font></i></a>, <a class="ref" href="finseq_1.html#T80" title="FINSEQ_1:th.80">FINSEQ_1:80</a></i>;<br/><a NAME="E4:31_3_1_1"/><i><font color="Green" title="E30">A10</font></i>: 
 <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"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E5:31_3_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i</font>
 <b>by </b><i><a class="txt" href="polynom3.html#E2:31_3"><i><font color="Green" title="E26">A6</font></i></a>, <a class="txt" href="polynom3.html#E1:31_3_1_1"><i><font color="Green" title="E27">A7</font></i></a>, <a class="ref" href="finseq_1.html#T80" title="FINSEQ_1:th.80">FINSEQ_1:80</a></i>;<br/><a NAME="E6:31_3_1_1"/><b>then </b><i><font color="Green" title="E31">A11</font></i>: 
 <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font></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> <font color="Maroon" title="c3">i</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E7:31_3_1_1"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">j</font> &amp; <font color="Maroon" title="c5">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">i</font> )
 <b>by </b><i><a class="txt" href="polynom3.html#E1:31_3"><i><font color="Green" title="E25">A5</font></i></a>, <a class="txt" href="polynom3.html#E2:31_3_1_1"><i><font color="Green" title="E28">A8</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/><a NAME="E8:31_3_1_1"/><b>then </b>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">j</font> &amp; <font color="Maroon" title="c5">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font> )
 <b>by </b><i><a class="txt" href="polynom3.html#E1:31_3_1_1"><i><font color="Green" title="E27">A7</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E9:31_3_1_1"/><b>then </b><i><font color="Green" title="E32">A12</font></i>: 
<font color="Maroon" title="c5">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <font color="Maroon" title="c2">f</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c6">Cf</font> =  <a href="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <font color="Maroon" title="c2">f</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="wsierp_1.html#K2" title="WSIERP_1:func.2">.</a> <font color="Maroon" title="c5">j</font> = 
 <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E1:31_3"><i><font color="Green" title="E25">A5</font></i></a>, <a class="txt" href="polynom3.html#E2:31_3_1_1"><i><font color="Green" title="E28">A8</font></i></a>, <a class="txt" href="polynom3.html#E3:31_3_1_1"><i><font color="Green" title="E29">A9</font></i></a>, <a class="txt" href="polynom3.html#E4:31_3_1_1"><i><font color="Green" title="E30">A10</font></i></a>, <a class="ref" href="card_3.html#D2" title="CARD_3:def.2">CARD_3:def 2</a></i>
<br/>.= 
 <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">/.</a> <font color="Maroon" title="c5">j</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E1:31_3"><i><font color="Green" title="E25">A5</font></i></a>, <a class="txt" href="polynom3.html#E2:31_3_1_1"><i><font color="Green" title="E28">A8</font></i></a>, <a class="txt" href="polynom3.html#E3:31_3_1_1"><i><font color="Green" title="E29">A9</font></i></a>, <a class="txt" href="polynom3.html#E4:31_3_1_1"><i><font color="Green" title="E30">A10</font></i></a>, <a class="ref" href="finseq_4.html#D4" title="FINSEQ_4:def.4">FINSEQ_4:def 4</a></i>
<br/>.= 
 <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="polynom1.html#K3" title="POLYNOM1:func.3">/.</a> <font color="Maroon" title="c5">j</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E1:31_3"><i><font color="Green" title="E25">A5</font></i></a>, <a class="txt" href="polynom3.html#E2:31_3_1_1"><i><font color="Green" title="E28">A8</font></i></a>, <a class="txt" href="polynom3.html#E3:31_3_1_1"><i><font color="Green" title="E29">A9</font></i></a>, <a class="txt" href="polynom3.html#E4:31_3_1_1"><i><font color="Green" title="E30">A10</font></i></a>, <a class="ref" href="finseq_4.html#T85" title="FINSEQ_4:th.85">FINSEQ_4:85</a></i>
<br/>.= 
 <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E9:31_3_1_1"><i><font color="Green" title="E32">A12</font></i></a>, <a class="ref" href="finseq_4.html#D4" title="FINSEQ_4:def.4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="wsierp_1.html#K2" title="WSIERP_1:func.2">.</a> <font color="Maroon" title="c5">j</font>
<b>by </b><i><a class="txt" href="polynom3.html#E9:31_3_1_1"><i><font color="Green" title="E32">A12</font></i></a>, <a class="ref" href="card_3.html#D2" title="CARD_3:def.2">CARD_3:def 2</a></i>
<br/>.= 
<font color="Maroon" title="c6">Cf</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c5">j</font>
<b>by </b><i><a class="txt" href="polynom3.html#E2:31"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="polynom3.html#E9:31_3_1_1"><i><font color="Green" title="E32">A12</font></i></a>, <a class="ref" href="finseq_4.html#D4" title="FINSEQ_4:def.4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">Cf</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c5">j</font>
<b>by </b><i><a class="txt" href="polynom3.html#E1:31_3"><i><font color="Green" title="E25">A5</font></i></a>, <a class="txt" href="polynom3.html#E2:31_3_1_1"><i><font color="Green" title="E28">A8</font></i></a>, <a class="txt" href="polynom3.html#E6:31_3_1_1"><i><font color="Green" title="E31">A11</font></i></a>, <a class="ref" href="finseq_4.html#T85" title="FINSEQ_4:th.85">FINSEQ_4:85</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="wsierp_1.html#K2" title="WSIERP_1:func.2">.</a> <font color="Maroon" title="c5">j</font>
<b>by </b><i><a class="txt" href="polynom3.html#E1:31_3"><i><font color="Green" title="E25">A5</font></i></a>, <a class="txt" href="polynom3.html#E2:31_3_1_1"><i><font color="Green" title="E28">A8</font></i></a>, <a class="txt" href="polynom3.html#E6:31_3_1_1"><i><font color="Green" title="E31">A11</font></i></a>, <a class="ref" href="finseq_4.html#D4" title="FINSEQ_4:def.4">FINSEQ_4:def 4</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_3_1_2"><b>suppose </b></a><a NAME="E1:31_3_1_2"/>
<font color="Maroon" title="c3">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font>
 ;<br/><div class="add"><a NAME="E2:31_3_1_2"/><b>then </b>
( <font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> &amp; <span class="p1">(<span class="default"><a href="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <font color="Maroon" title="c2">f</font> )
 <b>by </b><i><a class="txt" href="polynom3.html#E1:31"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="polynom3.html#E2:31_3"><i><font color="Green" title="E26">A6</font></i></a>, <a class="ref" href="finseq_2.html#T23" title="FINSEQ_2:th.23">FINSEQ_2:23</a></i>;<br/><b>hence </b><a NAME="E3:31_3_1_2"/>
<span class="p1">(<span class="default"><a href="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="wsierp_1.html#K2" title="WSIERP_1:func.2">.</a> <font color="Maroon" title="c5">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="wsierp_1.html#K2" title="WSIERP_1:func.2">.</a> <font color="Maroon" title="c5">j</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E8:31"/>
 <a href="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5" title="POLYNOM1:func.5">Card</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">i</font>
 <b>by </b><i><a class="txt" href="polynom3.html#E4:31"><i><font color="Green" title="E23">A3</font></i></a>, <a class="txt" href="polynom3.html#E6:31"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="finseq_2.html#T10" title="FINSEQ_2:th.10">FINSEQ_2:10</a></i>;<br/>


</div>
