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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="struct_0.html#L2" title="STRUCT_0:struct.2">ZeroStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">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>let </b><font color="Maroon" title="c3">p</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="E1:60"/><i><font color="Green" title="E47">A1</font></i>: 
<font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="algseq_1.html#K3" title="ALGSEQ_1:func.3">len</a> <font color="Maroon" title="c3">p</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c4">ps</font> =  <a href="uproots.html#K5" title="UPROOTS:func.5">poly_shift</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">n</font>;<br/>
<a NAME="E2:60"/><i><font color="Green" title="E48">A2</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="uproots.html#K5" title="UPROOTS:func.5">poly_shift</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:60_1"/>
<font color="Maroon" title="c5">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="uproots.html#K5" title="UPROOTS:func.5">poly_shift</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">n</font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c6">i</font> = <font color="Maroon" title="c5">z</font> 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>  ;<br/><a NAME="E3:60_1"/><i><font color="Green" title="E49">A3</font></i>: 
<font color="Maroon" title="c2">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <font color="Maroon" title="c6">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="algseq_1.html#K3" title="ALGSEQ_1:func.3">len</a> <font color="Maroon" title="c3">p</font>
 <b>by </b><i><a class="txt" href="uproots.html#E1:60"><i><font color="Green" title="E47">A1</font></i></a>, <a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="uproots.html#K5" title="UPROOTS:func.5">poly_shift</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">z</font> = 
<font color="Maroon" title="c3">p</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <font color="Maroon" title="c6">i</font></span>)</span>
<b>by </b><i><a class="ref" href="uproots.html#D6" target="_self" title="UPROOTS:def.6">Def6</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">L</font>
<b>by </b><i><a class="txt" href="uproots.html#E3:60_1"><i><font color="Green" title="E49">A3</font></i></a>, <a class="ref" href="algseq_1.html#T22" title="ALGSEQ_1:th.22">ALGSEQ_1:22</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E4:60"/><b>then </b>
 <a href="uproots.html#K5" title="UPROOTS:func.5">poly_shift</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">n</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="pboole.html#K9" title="PBOOLE:func.9">--&gt;</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">L</font></span>)</span>
 
<b>by </b><i><a class="txt" href="uproots.html#E2:60"><i><font color="Green" title="E48">A2</font></i></a>, <a class="ref" href="funcop_1.html#T17" title="FUNCOP_1:th.17">FUNCOP_1:17</a></i>;<br/>
<b>hence </b><a NAME="E5:60"/>
 <a href="uproots.html#K5" title="UPROOTS:func.5">poly_shift</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">n</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom3.html#K12" title="POLYNOM3:func.12">0_.</a> <font color="Maroon" title="c1">L</font>
 ;<br/>


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