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<b>let </b><font color="Maroon" title="c2">q1</font>, <font color="Maroon" title="c3">q2</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:9_1_2"/><i><font color="Green" title="E9">A3</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">q1</font> <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="c1">p</font>
 <b>and </b><br/><a NAME="E2:9_1_2"/><i><font color="Green" title="E10">A4</font></i>: 
for <font color="Olive" title="b1">n</font> being   <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>   st <font color="Olive" title="b1">n</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="c1">p</font> holds <br/><font color="Maroon" title="c2">q1</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Olive" title="b1">n</font></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
 <b>and </b><br/><a NAME="E3:9_1_2"/><i><font color="Green" title="E11">A5</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">q2</font> <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="c1">p</font>
 <b>and </b><br/><a NAME="E4:9_1_2"/><i><font color="Green" title="E12">A6</font></i>: 
for <font color="Olive" title="b1">n</font> being   <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>   st <font color="Olive" title="b1">n</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="c1">p</font> holds <br/><font color="Maroon" title="c3">q2</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Olive" title="b1">n</font></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
 ;<br/>

<a NAME="E5:9_1_2"/><i><font color="Green" title="E13">A7</font></i>: 
(  <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <font color="Maroon" title="c2">q1</font> <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="c1">p</font> &amp;  <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <font color="Maroon" title="c3">q2</font> <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="c1">p</font> )
 
<b>by </b><i><a class="txt" href="polynom5.html#E1:9_1_2"><i><font color="Green" title="E9">A3</font></i></a>, <a class="txt" href="polynom5.html#E3:9_1_2"><i><font color="Green" title="E11">A5</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="9_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">n</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="E1:9_1_2_1"/><i><font color="Green" title="E14">A8</font></i>: 
<font color="Maroon" title="c4">n</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="c1">p</font>
 ;<br/><b>hence </b><font color="Maroon" title="c2">q1</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c4">n</font> = 
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c4">n</font></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
<b>by </b><i><a class="txt" href="polynom5.html#E2:9_1_2"><i><font color="Green" title="E10">A4</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c3">q2</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c4">n</font>
<b>by </b><i><a class="txt" href="polynom5.html#E4:9_1_2"><i><font color="Green" title="E12">A6</font></i></a>, <a class="txt" href="polynom5.html#E1:9_1_2_1"><i><font color="Green" title="E14">A8</font></i></a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:9_1_2"/>
<font color="Maroon" title="c2">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q2</font>
 <b>by </b><i><a class="txt" href="polynom5.html#E5:9_1_2"><i><font color="Green" title="E13">A7</font></i></a>, <a class="ref" href="finseq_5.html#T13" title="FINSEQ_5:th.13">FINSEQ_5:13</a></i>;<br/>


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