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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="c1">L</font><br/>  for <font color="Olive" title="b3">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b3">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Olive" title="b1">p</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">m</font> &amp;  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Olive" title="b2">q</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">m</font> holds <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="Maroon" title="c1">L</font>  st <font color="Olive" title="b4">x</font> <a href="polynom8.html#R1" title="POLYNOM8:pred.1">is_primitive_root_of_degree</a> 2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b3">m</font> &amp;  <a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b3">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">L</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b3">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="polynom5.html#K4" title="POLYNOM5:func.4">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<font color="Olive" title="b1">p</font>,<font color="Olive" title="b4">x</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b3">m</font></span>)</span>)</span>)</span> <a href="lopban_3.html#K4" title="LOPBAN_3:func.4">*</a> <span class="p3">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<font color="Olive" title="b2">q</font>,<font color="Olive" title="b4">x</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b3">m</font></span>)</span>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b4">x</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b3">m</font></span>)</span>)</span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Olive" title="b2">q</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b1">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">m</font> &amp;  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c3">q</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">m</font> holds <br/> for <font color="Olive" title="b2">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b2">x</font> <a href="polynom8.html#R1" title="POLYNOM8:pred.1">is_primitive_root_of_degree</a> 2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b1">m</font> &amp;  <a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b1">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">L</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b1">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="polynom5.html#K4" title="POLYNOM5:func.4">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<font color="Maroon" title="c2">p</font>,<font color="Olive" title="b2">x</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b1">m</font></span>)</span>)</span>)</span> <a href="lopban_3.html#K4" title="LOPBAN_3:func.4">*</a> <span class="p3">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<font color="Maroon" title="c3">q</font>,<font color="Olive" title="b2">x</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b1">m</font></span>)</span>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">x</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b1">m</font></span>)</span>)</span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c3">q</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">m</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">m</font> &amp;  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c3">q</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">m</font> implies  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="c1">L</font>  st <font color="Olive" title="b1">x</font> <a href="polynom8.html#R1" title="POLYNOM8:pred.1">is_primitive_root_of_degree</a> 2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font> &amp;  <a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">L</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="polynom5.html#K4" title="POLYNOM5:func.4">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span> <a href="lopban_3.html#K4" title="LOPBAN_3:func.4">*</a> <span class="p3">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<font color="Maroon" title="c3">q</font>,<font color="Olive" title="b1">x</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c3">q</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:67"/><span class="lab"><font color="Green" title="E60">A1</font></span>: 
( <font color="Maroon" title="c4">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">m</font> &amp;  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c3">q</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">m</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="c1">L</font>  st <font color="Olive" title="b1">x</font> <a href="polynom8.html#R1" title="POLYNOM8:pred.1">is_primitive_root_of_degree</a> 2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font> &amp;  <a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">L</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="polynom5.html#K4" title="POLYNOM5:func.4">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span> <a href="lopban_3.html#K4" title="LOPBAN_3:func.4">*</a> <span class="p3">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<font color="Maroon" title="c3">q</font>,<font color="Olive" title="b1">x</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c3">q</font></span><br/>

<span class="kw">let </span><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="c1">L</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">x</font> <a href="polynom8.html#R1" title="POLYNOM8:pred.1">is_primitive_root_of_degree</a> 2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font> &amp;  <a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">L</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="polynom5.html#K4" title="POLYNOM5:func.4">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">x</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span> <a href="lopban_3.html#K4" title="LOPBAN_3:func.4">*</a> <span class="p3">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">x</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c3">q</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:67"/><span class="lab"><font color="Green" title="E61">A2</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="polynom8.html#R1" title="POLYNOM8:pred.1">is_primitive_root_of_degree</a> 2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">L</font> or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="polynom5.html#K4" title="POLYNOM5:func.4">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">x</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span> <a href="lopban_3.html#K4" title="LOPBAN_3:func.4">*</a> <span class="p3">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">x</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c3">q</font> )</span><br/>

<span class="kw">assume </span><a NAME="E3:67"/><span class="lab"><font color="Green" title="E62">A3</font></span>: 
 <a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">L</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="polynom5.html#K4" title="POLYNOM5:func.4">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">x</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span> <a href="lopban_3.html#K4" title="LOPBAN_3:func.4">*</a> <span class="p3">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">x</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c3">q</font></span><br/>

<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="polynom5.html#K4" title="POLYNOM5:func.4">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">x</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span> <a href="lopban_3.html#K4" title="LOPBAN_3:func.4">*</a> <span class="p3">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">x</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="polynom5.html#K4" title="POLYNOM5:func.4">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<span class="p2">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c3">q</font></span>)</span>,<font color="Maroon" title="c5">x</font>,<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom8.html#T34" target="_self" onmouseover="rs('polynom8/T34')" onmouseout="rh()">Th34</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="polynom5.html#K4" title="POLYNOM5:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="polynom5.html#K4" title="POLYNOM5:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E60">A1</font></span></a>, <a class="txt" href="#E2:67"><span class="lab"><font color="Green" title="E61">A2</font></span></a>, <a class="ref" href="polynom8.html#T43" target="_self" onmouseover="rs('polynom8/T43')" onmouseout="rh()">Th43</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span></span>)</span> <a href="polynom5.html#K4" title="POLYNOM5:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c3">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom8.html#T10" target="_self" onmouseover="rs('polynom8/T10')" onmouseout="rh()">Th10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="polynom5.html#K4" title="POLYNOM5:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c3">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:67"><span class="lab"><font color="Green" title="E62">A3</font></span></a>, <a class="ref" href="vectsp_1.html#D10" onmouseover="rs('vectsp_1/D10')" onmouseout="rh()">VECTSP_1:def 10</a></span>
<br/>.= 
<font color="Maroon" title="c2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c3">q</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom5.html#T27" onmouseover="rs('polynom5/T27')" onmouseout="rh()">POLYNOM5:27</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E5:67"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="polynom5.html#K4" title="POLYNOM5:func.4">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">x</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span> <a href="lopban_3.html#K4" title="LOPBAN_3:func.4">*</a> <span class="p3">(<span class="default"><a href="polynom8.html#K5" title="POLYNOM8:func.5">DFT</a> (<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">x</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">m</font></span>)</span>)</span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c3">q</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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