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<b>let </b><font color="Maroon" title="c4">f1</font>, <font color="Maroon" title="c5">f2</font> be   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">L</font>;<br/>

<b>given </b><font color="Maroon" title="c6">t1</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">L</font><b> such that </b><a NAME="E2:48_1_2"/><i><font color="Green" title="E44">A45</font></i>: 
( <font color="Maroon" title="c2">p</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <font color="Maroon" title="c6">t1</font> &amp;  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c6">t1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c3">s</font> )
 ;<br/>

<b>given </b><font color="Maroon" title="c7">t2</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">L</font><b> such that </b><a NAME="E4:48_1_2"/><i><font color="Green" title="E45">A46</font></i>: 
( <font color="Maroon" title="c2">p</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <font color="Maroon" title="c7">t2</font> &amp;  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c7">t2</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c3">s</font> )
 ;<br/>

<font color="Maroon" title="c5">f2</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c3">s</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <span class="p1">(<span class="default"><a href="polynom3.html#K9" title="POLYNOM3:func.9">0_.</a> <font color="Maroon" title="c1">L</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#T29" title="POLYNOM3:th.29">POLYNOM3:29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">t2</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c7">t2</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#T30" title="POLYNOM3:th.30">POLYNOM3:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <font color="Maroon" title="c6">t1</font></span>)</span> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <span class="p1">(<span class="default"><a href="bhsp_1.html#K6" title="BHSP_1:func.6">-</a> <font color="Maroon" title="c7">t2</font></span>)</span>
<b>by </b><i><a class="txt" href="hurwitz.html#E2:48_1_2"><i><font color="Green" title="E44">A45</font></i></a>, <a class="txt" href="hurwitz.html#E4:48_1_2"><i><font color="Green" title="E45">A46</font></i></a>, <a class="ref" href="polynom3.html#T26" title="POLYNOM3:th.26">POLYNOM3:26</a></i>
;<br/>
<b>then </b><i><font color="Green" title="E46">A47</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c3">s</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">t1</font> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <span class="p3">(<span class="default"><a href="bhsp_1.html#K6" title="BHSP_1:func.6">-</a> <font color="Maroon" title="c7">t2</font></span>)</span></span>)</span></span>)</span> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <span class="p1">(<span class="default"><a href="bhsp_1.html#K6" title="BHSP_1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#T26" title="POLYNOM3:th.26">POLYNOM3:26</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">t1</font> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <span class="p2">(<span class="default"><a href="bhsp_1.html#K6" title="BHSP_1:func.6">-</a> <font color="Maroon" title="c7">t2</font></span>)</span></span>)</span> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c3">s</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#T26" title="POLYNOM3:th.26">POLYNOM3:26</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">t1</font> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <span class="p2">(<span class="default"><a href="bhsp_1.html#K6" title="BHSP_1:func.6">-</a> <font color="Maroon" title="c7">t2</font></span>)</span></span>)</span> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <span class="p1">(<span class="default"><a href="polynom3.html#K9" title="POLYNOM3:func.9">0_.</a> <font color="Maroon" title="c1">L</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#T30" title="POLYNOM3:th.30">POLYNOM3:30</a></i>
<br/>.= 
<font color="Maroon" title="c6">t1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c7">t2</font>
<b>by </b><i><a class="ref" href="polynom3.html#T29" title="POLYNOM3:th.29">POLYNOM3:29</a></i>
;<br/>
<i><font color="Green" title="E47">A48</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c4">f1</font></span>)</span> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c3">s</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bhsp_1.html#K6" title="BHSP_1:func.6">-</a> <font color="Maroon" title="c4">f1</font></span>)</span> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c3">s</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#T33" title="POLYNOM3:th.33">POLYNOM3:33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c3">s</font></span>)</span>
<b>by </b><i><a class="ref" href="hurwitz.html#T12" target="_self" title="HURWITZ:th.12">Th12</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1_2_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:48_1_2_4"/><i><font color="Green" title="E48">A49</font></i>: 
<font color="Maroon" title="c4">f1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">f2</font>
 ;<br/><div><i><font color="Green" title="E49">A50</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1_2_4_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:48_1_2_4_1"/>
<font color="Maroon" title="c5">f2</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c4">f1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="polynom3.html#K9" title="POLYNOM3:func.9">0_.</a> <font color="Maroon" title="c1">L</font>
 ;<br/><b>then </b><font color="Maroon" title="c4">f1</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <span class="p2">(<span class="default"><a href="bhsp_1.html#K6" title="BHSP_1:func.6">-</a> <font color="Maroon" title="c4">f1</font></span>)</span></span>)</span> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <font color="Maroon" title="c4">f1</font>
<b>by </b><i><a class="ref" href="polynom3.html#T29" title="POLYNOM3:th.29">POLYNOM3:29</a></i>
<br/>.= 
<font color="Maroon" title="c5">f2</font> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c4">f1</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#T26" title="POLYNOM3:th.26">POLYNOM3:26</a></i>
<br/>.= 
<font color="Maroon" title="c5">f2</font> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <span class="p1">(<span class="default"><a href="polynom3.html#K9" title="POLYNOM3:func.9">0_.</a> <font color="Maroon" title="c1">L</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#T30" title="POLYNOM3:th.30">POLYNOM3:30</a></i>
;<br/><b>hence </b><a NAME="E3:48_1_2_4_1"/>
contradiction
 <b>by </b><i><a class="txt" href="hurwitz.html#E1:48_1_2_4"><i><font color="Green" title="E48">A49</font></i></a>, <a class="ref" href="polynom3.html#T29" title="POLYNOM3:th.29">POLYNOM3:29</a></i>;<br/></div><b>end;</b></div><b>then reconsider </b><font color="Maroon" title="c8">d</font> =  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c4">f1</font></span>)</span>, <font color="Maroon" title="c9">degs</font> =  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c3">s</font> as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> <b>by </b><i><a class="txt" href="hurwitz.html#E1:48"><i><font color="Green" title="E43">A1</font></i></a>, <a class="txt" href="hurwitz.html#E31"><i><font color="Green" title="E29">Lm9</font></i></a></i>;<br/><a NAME="E4:48_1_2_4"/><i><font color="Green" title="E50">A51</font></i>: 
 <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">t1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c7">t2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c9">degs</font>
 <b>by </b><i><a class="txt" href="hurwitz.html#E1:48"><i><font color="Green" title="E43">A1</font></i></a>, <a class="txt" href="hurwitz.html#E7:48_1_2"><i><font color="Green" title="E47">A48</font></i></a>, <a class="txt" href="hurwitz.html#E6:48_1_2"><i><font color="Green" title="E46">A47</font></i></a>, <a class="txt" href="hurwitz.html#E2:48_1_2_4"><i><font color="Green" title="E49">A50</font></i></a>, <a class="ref" href="hurwitz.html#T23" target="_self" title="HURWITZ:th.23">Th23</a></i>;<br/><a NAME="E5:48_1_2_4"/>
 <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">t1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c7">t2</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <span class="p1">(<span class="default"><a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c6">t1</font></span>)</span>,<span class="p1">(<span class="default"><a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <span class="p2">(<span class="default"><a href="bhsp_1.html#K6" title="BHSP_1:func.6">-</a> <font color="Maroon" title="c7">t2</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="hurwitz.html#T22" target="_self" title="HURWITZ:th.22">Th22</a></i>;<br/><a NAME="E6:48_1_2_4"/><b>then </b><i><font color="Green" title="E51">A52</font></i>: 
 <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">t1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c7">t2</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <span class="p1">(<span class="default"><a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c6">t1</font></span>)</span>,<span class="p1">(<span class="default"><a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c7">t2</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom4.html#T11" title="POLYNOM4:th.11">POLYNOM4:11</a></i>;<br/><a NAME="E7:48_1_2_4"/>
 <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">t1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c7">t2</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">degs</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1_2_4_2"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_1_2_4_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:48_1_2_4_2_1"/>
(  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <span class="p1">(<span class="default"><a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c6">t1</font></span>)</span>,<span class="p1">(<span class="default"><a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c7">t2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c6">t1</font> or  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <span class="p1">(<span class="default"><a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c6">t1</font></span>)</span>,<span class="p1">(<span class="default"><a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c7">t2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c7">t2</font> )
 </span><b>by </b><i><a class="ref" href="xxreal_0.html#T16" title="XXREAL_0:th.16">XXREAL_0:16</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_1_2_4_2_1_1"><b>suppose </b></a><a NAME="E1:48_1_2_4_2_1_1"/>
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <span class="p1">(<span class="default"><a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c6">t1</font></span>)</span>,<span class="p1">(<span class="default"><a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c7">t2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c6">t1</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:48_1_2_4_2_1_1"/>
 <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">t1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c7">t2</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">degs</font>
 <b>by </b><i><a class="txt" href="hurwitz.html#E6:48_1_2_4"><i><font color="Green" title="E51">A52</font></i></a>, <a class="txt" href="hurwitz.html#E2:48_1_2"><i><font color="Green" title="E44">A45</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_1_2_4_2_1_2"><b>suppose </b></a><a NAME="E1:48_1_2_4_2_1_2"/>
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <span class="p1">(<span class="default"><a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c6">t1</font></span>)</span>,<span class="p1">(<span class="default"><a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c7">t2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c7">t2</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:48_1_2_4_2_1_2"/>
 <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">t1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c7">t2</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">degs</font>
 <b>by </b><i><a class="txt" href="hurwitz.html#E6:48_1_2_4"><i><font color="Green" title="E51">A52</font></i></a>, <a class="txt" href="hurwitz.html#E4:48_1_2"><i><font color="Green" title="E45">A46</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><b>hence </b><a NAME="E8:48_1_2_4"/>
contradiction
 <b>by </b><i><a class="txt" href="hurwitz.html#E4:48_1_2_4"><i><font color="Green" title="E50">A51</font></i></a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E9:48_1_2"/>
<font color="Maroon" title="c4">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font>
 ;<br/>


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