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<b>let </b><font color="Maroon" title="c1">m</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">L</font> being  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a><br/> for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</font> being  <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b1">L</font><br/> for <font color="Olive" title="b4">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font> holds  <span class="p1">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Olive" title="b2">p</font>,<font color="Olive" title="b4">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="polynom8.html#K2" title="POLYNOM8:func.2">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Olive" title="b3">q</font>,<font color="Olive" title="b4">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">p</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Olive" title="b3">q</font></span>)</span>,<font color="Olive" title="b4">x</font>,<font color="Maroon" title="c1">m</font></span><br/><b>let </b><font color="Maroon" title="c2">L</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being  <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c2">L</font><br/> for <font color="Olive" title="b3">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> holds  <span class="p1">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b3">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="polynom8.html#K2" title="POLYNOM8:func.2">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Olive" title="b2">q</font></span>)</span>,<font color="Olive" title="b3">x</font>,<font color="Maroon" title="c1">m</font></span><br/><b>let </b><font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">q</font> be   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c2">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> holds  <span class="p1">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c3">p</font>,<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="polynom8.html#K2" title="POLYNOM8:func.2">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c4">q</font>,<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c4">q</font></span>)</span>,<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">m</font></span><br/><b>let </b><font color="Maroon" title="c5">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="polynom8.html#K2" title="POLYNOM8:func.2">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c4">q</font></span>)</span>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span><br/>







<b>set </b><font color="Maroon" title="c6">ep</font> =  <a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font>;<br/>
<b>set </b><font color="Maroon" title="c7">eq</font> =  <a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font>;<br/>
<b>set </b><font color="Maroon" title="c8">epq</font> =  <a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c4">q</font></span>)</span>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font>;<br/>
<i><font color="Green" title="E51">A1</font></i>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="polynom8.html#K2" title="POLYNOM8:func.2">*</a> <span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span></span>)</span> = 
 <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/>.= 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c4">q</font></span>)</span>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span>
<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="54_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">u'</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c9">u'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="polynom8.html#K2" title="POLYNOM8:func.2">*</a> <span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c4">q</font></span>)</span>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="polynom8.html#K2" title="POLYNOM8:func.2">*</a> <span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><b>assume </b><a NAME="E1:54_2"/>
<font color="Maroon" title="c9">u'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="polynom8.html#K2" title="POLYNOM8:func.2">*</a> <span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c4">q</font></span>)</span>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="polynom8.html#K2" title="POLYNOM8:func.2">*</a> <span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><b>then reconsider </b><font color="Maroon" title="c10">u</font> = <font color="Maroon" title="c9">u'</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <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="hsNdiv(this)" href="javascript:()" title="54_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:54_2_1"/>
( <font color="Maroon" title="c10">u</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">m</font> or <font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">u</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="54_2_1_1"><b>suppose </b></a><a NAME="E1:54_2_1_1"/><i><font color="Green" title="E52">A2</font></i>: 
<font color="Maroon" title="c10">u</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c4">q</font></span>)</span>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="polynom8.html#K2" title="POLYNOM8:func.2">*</a> <span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c4">q</font></span>)</span>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">u'</font> = 
 <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="binom.html#K2" title="BINOM:func.2">|^</a> <font color="Maroon" title="c10">u</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom8.html#D7" target="_self" title="POLYNOM8:def.7">Def7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <font color="Maroon" title="c3">p</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="binom.html#K2" title="BINOM:func.2">|^</a> <font color="Maroon" title="c10">u</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <font color="Maroon" title="c4">q</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="binom.html#K2" title="BINOM:func.2">|^</a> <font color="Maroon" title="c10">u</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom4.html#T27" title="POLYNOM4:th.27">POLYNOM4:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c10">u</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <font color="Maroon" title="c4">q</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="binom.html#K2" title="BINOM:func.2">|^</a> <font color="Maroon" title="c10">u</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom8.html#E1:54_2_1_1"><i><font color="Green" title="E52">A2</font></i></a>, <a class="ref" href="polynom8.html#D7" target="_self" title="POLYNOM8:def.7">Def7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c10">u</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c10">u</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom8.html#E1:54_2_1_1"><i><font color="Green" title="E52">A2</font></i></a>, <a class="ref" href="polynom8.html#D7" target="_self" title="POLYNOM8:def.7">Def7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="polynom8.html#K2" title="POLYNOM8:func.2">*</a> <span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">u'</font>
<b>by </b><i><a class="ref" href="polynom8.html#D2" target="_self" title="POLYNOM8:def.2">Def2</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="54_2_1_2"><b>suppose </b></a><a NAME="E1:54_2_1_2"/><i><font color="Green" title="E52">A3</font></i>: 
<font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">u</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="polynom8.html#K2" title="POLYNOM8:func.2">*</a> <span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c4">q</font></span>)</span>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="polynom8.html#K2" title="POLYNOM8:func.2">*</a> <span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">u'</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c10">u</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c10">u</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom8.html#D2" target="_self" title="POLYNOM8:def.2">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c10">u</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom8.html#E1:54_2_1_2"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="polynom8.html#D7" target="_self" title="POLYNOM8:def.7">Def7</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font>
<b>by </b><i><a class="ref" href="vectsp_1.html#T36" title="VECTSP_1:th.36">VECTSP_1:36</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c4">q</font></span>)</span>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">u'</font>
<b>by </b><i><a class="txt" href="polynom8.html#E1:54_2_1_2"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="polynom8.html#D7" target="_self" title="POLYNOM8:def.7">Def7</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:54"/>
<span class="p1">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="polynom8.html#K2" title="POLYNOM8:func.2">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom8.html#K6" title="POLYNOM8:func.6">DFT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Maroon" title="c4">q</font></span>)</span>,<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">m</font>
 <b>by </b><i><a class="txt" href="polynom8.html#E1:54"><i><font color="Green" title="E51">A1</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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