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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a>  <a href="rlvect_1.html#L1">LoopStr</a> ;<br/><b>let </b><font color="Maroon">p1</font> be   <a href="polynom3.html#NM1">Polynomial</a> of <font color="Maroon">L</font>, <font color="Maroon">p2</font> be   <a href="polynom3.html#NM1">Polynomial</a> of <font color="Maroon">L</font>;<br/>



<b>assume </b><a NAME="E1:32"/>
 <a href="hurwitz.html#NK3" target="_self">deg</a> <font color="Maroon">p1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="hurwitz.html#NK3" target="_self">deg</a> <font color="Maroon">p2</font>
 ;<br/>

<a NAME="E2:32"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="hurwitz.html#NK3" target="_self">deg</a> <span class="p1">(<span class="default"><font color="Maroon">p1</font> <a href="polynom3.html#K8">+</a> <font color="Maroon">p2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="square_1.html#K2">max</a> <span class="p2">(<span class="default"><a href="algseq_1.html#K3">len</a> <font color="Maroon">p1</font></span>)</span>,<span class="p2">(<span class="default"><a href="algseq_1.html#K3">len</a> <font color="Maroon">p2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i><a class="ref" href="polynom4.html#T10">POLYNOM4:10</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:32_1"/>
(  <a href="square_1.html#K2">max</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K3">len</a> <font color="Maroon">p1</font></span>)</span>,<span class="p1">(<span class="default"><a href="algseq_1.html#K3">len</a> <font color="Maroon">p2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="algseq_1.html#K3">len</a> <font color="Maroon">p1</font> or  <a href="square_1.html#K2">max</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K3">len</a> <font color="Maroon">p1</font></span>)</span>,<span class="p1">(<span class="default"><a href="algseq_1.html#K3">len</a> <font color="Maroon">p2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="algseq_1.html#K3">len</a> <font color="Maroon">p2</font> )
 </span><b>by </b><i><a class="ref" href="square_1.html#T49">SQUARE_1:49</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_1_1"><b>suppose </b></a><a NAME="E1:32_1_1"/><i><font color="Green">E30</font></i>: 
 <a href="square_1.html#K2">max</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K3">len</a> <font color="Maroon">p1</font></span>)</span>,<span class="p1">(<span class="default"><a href="algseq_1.html#K3">len</a> <font color="Maroon">p2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="algseq_1.html#K3">len</a> <font color="Maroon">p1</font>
 ;<br/><div class="add"><a NAME="E2:32_1_1"/><b>then </b>
 <a href="algseq_1.html#K3">len</a> <font color="Maroon">p2</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="algseq_1.html#K3">len</a> <font color="Maroon">p1</font>
 <b>by </b><i><a class="ref" href="square_1.html#T46">SQUARE_1:46</a></i>;<br/><a NAME="E3:32_1_1"/><b>then </b><i><font color="Green">E31</font></i>: 
 <a href="hurwitz.html#NK3" target="_self">deg</a> <font color="Maroon">p2</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="hurwitz.html#NK3" target="_self">deg</a> <font color="Maroon">p1</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><b>thus </b><a NAME="E4:32_1_1"/>
 <a href="hurwitz.html#NK3" target="_self">deg</a> <span class="p1">(<span class="default"><font color="Maroon">p1</font> <a href="polynom3.html#K8">+</a> <font color="Maroon">p2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xxreal_0.html#K4">max</a> <span class="p1">(<span class="default"><a href="hurwitz.html#NK3" target="_self">deg</a> <font color="Maroon">p1</font></span>)</span>,<span class="p1">(<span class="default"><a href="hurwitz.html#NK3" target="_self">deg</a> <font color="Maroon">p2</font></span>)</span>
 <b>by </b><i><a class="txt" href="hurwitz.html#E1:32_1_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="hurwitz.html#E3:32_1_1"><i><font color="Green">E31</font></i></a>, , <a class="ref" href="xxreal_0.html#D9">XXREAL_0:def 9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_1_2"><b>suppose </b></a><a NAME="E1:32_1_2"/><i><font color="Green">E34</font></i>: 
 <a href="square_1.html#K2">max</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K3">len</a> <font color="Maroon">p1</font></span>)</span>,<span class="p1">(<span class="default"><a href="algseq_1.html#K3">len</a> <font color="Maroon">p2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="algseq_1.html#K3">len</a> <font color="Maroon">p2</font>
 ;<br/><div class="add"><a NAME="E2:32_1_2"/><b>then </b>
 <a href="algseq_1.html#K3">len</a> <font color="Maroon">p1</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="algseq_1.html#K3">len</a> <font color="Maroon">p2</font>
 <b>by </b><i><a class="ref" href="square_1.html#T46">SQUARE_1:46</a></i>;<br/><a NAME="E3:32_1_2"/><b>then </b><i><font color="Green">E36</font></i>: 
 <a href="hurwitz.html#NK3" target="_self">deg</a> <font color="Maroon">p1</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="hurwitz.html#NK3" target="_self">deg</a> <font color="Maroon">p2</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><b>thus </b><a NAME="E4:32_1_2"/>
 <a href="hurwitz.html#NK3" target="_self">deg</a> <span class="p1">(<span class="default"><font color="Maroon">p1</font> <a href="polynom3.html#K8">+</a> <font color="Maroon">p2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xxreal_0.html#K4">max</a> <span class="p1">(<span class="default"><a href="hurwitz.html#NK3" target="_self">deg</a> <font color="Maroon">p1</font></span>)</span>,<span class="p1">(<span class="default"><a href="hurwitz.html#NK3" target="_self">deg</a> <font color="Maroon">p2</font></span>)</span>
 <b>by </b><i>, , , <a class="ref" href="xxreal_0.html#D9">XXREAL_0:def 9</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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