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<b>let </b><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">k</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c3">n</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <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> ;<br/>





<b>assume </b><a NAME="E1:41"/><i><font color="Green" title="E33">A1</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 4
 ;<br/>

<a NAME="E2:41"/><b>then </b>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">m</font>
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E3:41"/><b>then </b>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">m</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E4:41"/><b>then </b>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">m</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E5:41"/><b>then </b>
<span class="p1">(<span class="default"><a href="idea_1.html#K12" title="IDEA_1:func.12">IDEAoperationB</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binarith.html#K7" title="BINARITH:func.7">Absval</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1</span>)</span></span>)</span> <a href="idea_1.html#K3" title="IDEA_1:func.3">'xor'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p3">(<span class="default"><a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p4">(<span class="default"><a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p5">(<span class="default"><a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p0">(<span class="default"><a href="binarith.html#K7" title="BINARITH:func.7">Absval</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1</span>)</span></span>)</span> <a href="idea_1.html#K3" title="IDEA_1:func.3">'xor'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 5</span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span>,<span class="p5">(<span class="default"><a href="binarith.html#K7" title="BINARITH:func.7">Absval</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2</span>)</span></span>)</span> <a href="idea_1.html#K3" title="IDEA_1:func.3">'xor'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 4</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 6</span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="idea_1.html#D12" target="_self" title="IDEA_1:def.12">Def12</a></i>;<br/>
<a NAME="E6:41"/><b>then </b><i><font color="Green" title="E34">A2</font></i>: 
<span class="p1">(<span class="default"><a href="idea_1.html#K12" title="IDEA_1:func.12">IDEAoperationB</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 2 <a href="series_1.html#K3" title="SERIES_1:func.3">to_power</a> <font color="Maroon" title="c3">n</font>
 
<b>by </b><i><a class="ref" href="binari_3.html#T1" title="BINARI_3:th.1">BINARI_3:1</a></i>;<br/>
<a NAME="E7:41"/>
2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">m</font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E1:41"><i><font color="Green" title="E33">A1</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E8:41"/><b>then </b>
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">m</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E9:41"/><b>then </b>
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">m</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E10:41"/><b>then </b>
<span class="p1">(<span class="default"><a href="idea_1.html#K12" title="IDEA_1:func.12">IDEAoperationB</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binarith.html#K7" title="BINARITH:func.7">Absval</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2</span>)</span></span>)</span> <a href="idea_1.html#K3" title="IDEA_1:func.3">'xor'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p3">(<span class="default"><a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p4">(<span class="default"><a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p5">(<span class="default"><a href="binarith.html#K7" title="BINARITH:func.7">Absval</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1</span>)</span></span>)</span> <a href="idea_1.html#K3" title="IDEA_1:func.3">'xor'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 5</span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span>,<span class="p4">(<span class="default"><a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p5">(<span class="default"><a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p0">(<span class="default"><a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p1">(<span class="default"><a href="binarith.html#K7" title="BINARITH:func.7">Absval</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1</span>)</span></span>)</span> <a href="idea_1.html#K3" title="IDEA_1:func.3">'xor'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 5</span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span>,<span class="p0">(<span class="default"><a href="binarith.html#K7" title="BINARITH:func.7">Absval</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2</span>)</span></span>)</span> <a href="idea_1.html#K3" title="IDEA_1:func.3">'xor'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 4</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 6</span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="idea_1.html#D12" target="_self" title="IDEA_1:def.12">Def12</a></i>;<br/>
<a NAME="E11:41"/><b>then </b><i><font color="Green" title="E35">A3</font></i>: 
<span class="p1">(<span class="default"><a href="idea_1.html#K12" title="IDEA_1:func.12">IDEAoperationB</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 2 <a href="series_1.html#K3" title="SERIES_1:func.3">to_power</a> <font color="Maroon" title="c3">n</font>
 
<b>by </b><i><a class="ref" href="binari_3.html#T1" title="BINARI_3:th.1">BINARI_3:1</a></i>;<br/>
<a NAME="E12:41"/>
3 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">m</font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E1:41"><i><font color="Green" title="E33">A1</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E13:41"/><b>then </b>
3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">m</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E14:41"/><b>then </b>
3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">m</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E15:41"/><b>then </b>
<span class="p1">(<span class="default"><a href="idea_1.html#K12" title="IDEA_1:func.12">IDEAoperationB</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binarith.html#K7" title="BINARITH:func.7">Absval</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 3</span>)</span></span>)</span> <a href="idea_1.html#K3" title="IDEA_1:func.3">'xor'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p3">(<span class="default"><a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p4">(<span class="default"><a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p5">(<span class="default"><a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p0">(<span class="default"><a href="binarith.html#K7" title="BINARITH:func.7">Absval</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1</span>)</span></span>)</span> <a href="idea_1.html#K3" title="IDEA_1:func.3">'xor'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 5</span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span>,<span class="p5">(<span class="default"><a href="binarith.html#K7" title="BINARITH:func.7">Absval</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2</span>)</span></span>)</span> <a href="idea_1.html#K3" title="IDEA_1:func.3">'xor'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 4</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 6</span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="idea_1.html#D12" target="_self" title="IDEA_1:def.12">Def12</a></i>;<br/>
<a NAME="E16:41"/><b>then </b><i><font color="Green" title="E36">A4</font></i>: 
<span class="p1">(<span class="default"><a href="idea_1.html#K12" title="IDEA_1:func.12">IDEAoperationB</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 3 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 2 <a href="series_1.html#K3" title="SERIES_1:func.3">to_power</a> <font color="Maroon" title="c3">n</font>
 
<b>by </b><i><a class="ref" href="binari_3.html#T1" title="BINARI_3:th.1">BINARI_3:1</a></i>;<br/>
<a NAME="E17:41"/>
4 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">m</font></span>)</span>
 
<b>by </b><i><a class="txt" href="idea_1.html#E1:41"><i><font color="Green" title="E33">A1</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E18:41"/><b>then </b>
4 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">m</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E19:41"/><b>then </b>
<span class="p1">(<span class="default"><a href="idea_1.html#K12" title="IDEA_1:func.12">IDEAoperationB</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binarith.html#K7" title="BINARITH:func.7">Absval</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 4</span>)</span></span>)</span> <a href="idea_1.html#K3" title="IDEA_1:func.3">'xor'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p3">(<span class="default"><a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p4">(<span class="default"><a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p5">(<span class="default"><a href="binarith.html#K7" title="BINARITH:func.7">Absval</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1</span>)</span></span>)</span> <a href="idea_1.html#K3" title="IDEA_1:func.3">'xor'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 5</span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span>,<span class="p4">(<span class="default"><a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p5">(<span class="default"><a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p0">(<span class="default"><a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p1">(<span class="default"><a href="binarith.html#K7" title="BINARITH:func.7">Absval</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1</span>)</span></span>)</span> <a href="idea_1.html#K3" title="IDEA_1:func.3">'xor'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 5</span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span>,<span class="p0">(<span class="default"><a href="binarith.html#K7" title="BINARITH:func.7">Absval</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2</span>)</span></span>)</span> <a href="idea_1.html#K3" title="IDEA_1:func.3">'xor'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 4</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 6</span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="idea_1.html#D12" target="_self" title="IDEA_1:def.12">Def12</a></i>;<br/>
<a NAME="E20:41"/><b>then </b>
<span class="p1">(<span class="default"><a href="idea_1.html#K12" title="IDEA_1:func.12">IDEAoperationB</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 4 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 2 <a href="series_1.html#K3" title="SERIES_1:func.3">to_power</a> <font color="Maroon" title="c3">n</font>
 
<b>by </b><i><a class="ref" href="binari_3.html#T1" title="BINARI_3:th.1">BINARI_3:1</a></i>;<br/>
<b>hence </b><a NAME="E21:41"/>
( <span class="p1">(<span class="default"><a href="idea_1.html#K12" title="IDEA_1:func.12">IDEAoperationB</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c3">n</font> &amp; <span class="p1">(<span class="default"><a href="idea_1.html#K12" title="IDEA_1:func.12">IDEAoperationB</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c3">n</font> &amp; <span class="p1">(<span class="default"><a href="idea_1.html#K12" title="IDEA_1:func.12">IDEAoperationB</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 3 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c3">n</font> &amp; <span class="p1">(<span class="default"><a href="idea_1.html#K12" title="IDEA_1:func.12">IDEAoperationB</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">n</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 4 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c3">n</font> )
 <b>by </b><i><a class="txt" href="idea_1.html#E6:41"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="idea_1.html#E11:41"><i><font color="Green" title="E35">A3</font></i></a>, <a class="txt" href="idea_1.html#E16:41"><i><font color="Green" title="E36">A4</font></i></a>, <a class="ref" href="idea_1.html#D3" target="_self" title="IDEA_1:def.3">Def3</a></i>;<br/>


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