<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a>  <a href="rlvect_1.html#L1" title="RLVECT_1:struct.1">LoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">p1</font>, <font color="Maroon" title="c3">p2</font> be   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">L</font>;<br/>



<b>assume </b><a NAME="E1:32"/>
 <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c2">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c3">p2</font>
 ;<br/>

<a NAME="E2:32"/><b>then </b><i><font color="Green" title="E30">A1</font></i>: 
 <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="normsp_1.html#K3" title="NORMSP_1:func.3">+</a> <font color="Maroon" title="c3">p2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <span class="p2">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">p1</font></span>)</span>,<span class="p2">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c3">p2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 
<b>by </b><i><a class="ref" href="polynom4.html#T10" title="POLYNOM4:th.10">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="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">p1</font></span>)</span>,<span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c3">p2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">p1</font> or  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">p1</font></span>)</span>,<span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c3">p2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c3">p2</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="32_1_1"><b>suppose </b></a><a NAME="E1:32_1_1"/><i><font color="Green" title="E31">A2</font></i>: 
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">p1</font></span>)</span>,<span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c3">p2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">p1</font>
 ;<br/><div class="add"><a NAME="E2:32_1_1"/><b>then </b>
 <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c3">p2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">p1</font>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T25" title="XXREAL_0:th.25">XXREAL_0:25</a></i>;<br/><a NAME="E3:32_1_1"/><b>then </b>
 <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c3">p2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c2">p1</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/><b>hence </b><a NAME="E4:32_1_1"/>
 <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="normsp_1.html#K3" title="NORMSP_1:func.3">+</a> <font color="Maroon" title="c3">p2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c2">p1</font></span>)</span>,<span class="p1">(<span class="default"><a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c3">p2</font></span>)</span>
 <b>by </b><i><a class="txt" href="hurwitz.html#E2:32"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="hurwitz.html#E1:32_1_1"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="xxreal_0.html#D9" title="XXREAL_0:def.9">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" title="E31">A3</font></i>: 
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">p1</font></span>)</span>,<span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c3">p2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c3">p2</font>
 ;<br/><div class="add"><a NAME="E2:32_1_2"/><b>then </b>
 <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">p1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c3">p2</font>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T25" title="XXREAL_0:th.25">XXREAL_0:25</a></i>;<br/><a NAME="E3:32_1_2"/><b>then </b>
 <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c2">p1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c3">p2</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/><b>hence </b><a NAME="E4:32_1_2"/>
 <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="normsp_1.html#K3" title="NORMSP_1:func.3">+</a> <font color="Maroon" title="c3">p2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c2">p1</font></span>)</span>,<span class="p1">(<span class="default"><a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c3">p2</font></span>)</span>
 <b>by </b><i><a class="txt" href="hurwitz.html#E2:32"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="hurwitz.html#E1:32_1_2"><i><font color="Green" title="E31">A3</font></i></a>, <a class="ref" href="xxreal_0.html#D9" title="XXREAL_0:def.9">XXREAL_0:def 9</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
