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<b>let </b><font color="Maroon" title="c1">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>let </b><font color="Maroon" title="c2">m</font>, <font color="Maroon" title="c3">k1</font>, <font color="Maroon" title="c4">k2</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>assume </b><b>that </b><br/><a NAME="E1:47"/><i><font color="Green" title="E38">A1</font></i>: 
( <span class="p1">(<span class="default">2 <a href="series_1.html#K3" title="SERIES_1:func.3">to_power</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 4 &amp; <font color="Maroon" title="c2">m</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c2">m</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c2">m</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c2">m</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c1">n</font> )
 <b>and </b><br/><a NAME="E2:47"/><i><font color="Green" title="E39">A2</font></i>: 
<font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K10" title="IDEA_1:func.10">INV_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1</span>)</span>,<font color="Maroon" title="c1">n</font>
 <b>and </b><br/><a NAME="E3:47"/><i><font color="Green" title="E40">A3</font></i>: 
<font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K6" title="IDEA_1:func.6">NEG_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3</span>)</span>,<font color="Maroon" title="c1">n</font>
 <b>and </b><br/><a NAME="E4:47"/><i><font color="Green" title="E41">A4</font></i>: 
<font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K6" title="IDEA_1:func.6">NEG_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2</span>)</span>,<font color="Maroon" title="c1">n</font>
 <b>and </b><br/><a NAME="E5:47"/><i><font color="Green" title="E42">A5</font></i>: 
<font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K10" title="IDEA_1:func.10">INV_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4</span>)</span>,<font color="Maroon" title="c1">n</font>
 ;<br/>

<a NAME="E6:47"/><i><font color="Green" title="E43">A6</font></i>: 
<font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c1">n</font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="idea_1.html#E2:47"><i><font color="Green" title="E39">A2</font></i></a>, <a class="ref" href="idea_1.html#D10" target="_self" title="IDEA_1:def.10">Def10</a></i>;<br/>
<a NAME="E7:47"/><i><font color="Green" title="E44">A7</font></i>: 
<font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4 <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c1">n</font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="idea_1.html#E5:47"><i><font color="Green" title="E42">A5</font></i></a>, <a class="ref" href="idea_1.html#D10" target="_self" title="IDEA_1:def.10">Def10</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">I1</font> being    <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> <b> such that </b><br/><a NAME="E9:47"/><i><font color="Green" title="E45">A8</font></i>: 
<font color="Maroon" title="c5">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K13" title="IDEA_1:func.13">IDEAoperationC</a> <font color="Maroon" title="c2">m</font>
 ;<br/>
<b>consider </b><font color="Maroon" title="c6">I2</font> being    <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> <b> such that </b><br/><a NAME="E11:47"/><i><font color="Green" title="E46">A9</font></i>: 
<font color="Maroon" title="c6">I2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K11" title="IDEA_1:func.11">IDEAoperationA</a> <font color="Maroon" title="c5">I1</font>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c1">n</font>
 ;<br/>
<a NAME="E12:47"/><i><font color="Green" title="E47">A10</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">I2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">I1</font> &amp; ( for <font color="Olive" title="b1">i</font> being   <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>   st <font color="Olive" title="b1">i</font> <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="c5">I1</font> holds <br/>( ( <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies <font color="Maroon" title="c6">I2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">I1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1</span>)</span>,<font color="Maroon" title="c1">n</font> ) &amp; ( <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 implies <font color="Maroon" title="c6">I2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">I1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2</span>)</span>,<font color="Maroon" title="c1">n</font> ) &amp; ( <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 implies <font color="Maroon" title="c6">I2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">I1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3</span>)</span>,<font color="Maroon" title="c1">n</font> ) &amp; ( <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 implies <font color="Maroon" title="c6">I2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">I1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4</span>)</span>,<font color="Maroon" title="c1">n</font> ) &amp; ( <font color="Olive" title="b1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Olive" title="b1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 &amp; <font color="Olive" title="b1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 3 &amp; <font color="Olive" title="b1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 4 implies <font color="Maroon" title="c6">I2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">I1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Olive" title="b1">i</font> ) ) ) )
 
<b>by </b><i><a class="txt" href="idea_1.html#E11:47"><i><font color="Green" title="E46">A9</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self" title="IDEA_1:def.11">Def11</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">I3</font> being    <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> <b> such that </b><br/><a NAME="E14:47"/><i><font color="Green" title="E48">A11</font></i>: 
<font color="Maroon" title="c7">I3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K13" title="IDEA_1:func.13">IDEAoperationC</a> <font color="Maroon" title="c6">I2</font>
 ;<br/>
<a NAME="E15:47"/><i><font color="Green" title="E49">A12</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">I3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">I2</font> &amp; ( for <font color="Olive" title="b1">i</font> being   <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>   st <font color="Olive" title="b1">i</font> <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="c6">I2</font> holds <br/>( ( <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 implies <font color="Maroon" title="c7">I3</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">I2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3 ) &amp; ( <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 implies <font color="Maroon" title="c7">I3</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">I2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2 ) &amp; ( <font color="Olive" title="b1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 &amp; <font color="Olive" title="b1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 3 implies <font color="Maroon" title="c7">I3</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">I2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Olive" title="b1">i</font> ) ) ) )
 
<b>by </b><i><a class="txt" href="idea_1.html#E14:47"><i><font color="Green" title="E48">A11</font></i></a>, <a class="ref" href="idea_1.html#D13" target="_self" title="IDEA_1:def.13">Def13</a>, <a class="txt" href="idea_1.html#E44"><i><font color="Green" title="E33">Lm3</font></i></a>, <a class="txt" href="idea_1.html#E45"><i><font color="Green" title="E34">Lm4</font></i></a>, <a class="txt" href="idea_1.html#E46"><i><font color="Green" title="E35">Lm5</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">I4</font> being    <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> <b> such that </b><br/><a NAME="E17:47"/><i><font color="Green" title="E50">A13</font></i>: 
<font color="Maroon" title="c8">I4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K11" title="IDEA_1:func.11">IDEAoperationA</a> <font color="Maroon" title="c7">I3</font>,<font color="Maroon" title="c4">k2</font>,<font color="Maroon" title="c1">n</font>
 ;<br/>
<a NAME="E18:47"/><i><font color="Green" title="E51">A14</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">I4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">I3</font> &amp; ( for <font color="Olive" title="b1">i</font> being   <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>   st <font color="Olive" title="b1">i</font> <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="c7">I3</font> holds <br/>( ( <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies <font color="Maroon" title="c8">I4</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">I3</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1</span>)</span>,<font color="Maroon" title="c1">n</font> ) &amp; ( <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 implies <font color="Maroon" title="c8">I4</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">I3</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2</span>)</span>,<font color="Maroon" title="c1">n</font> ) &amp; ( <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 implies <font color="Maroon" title="c8">I4</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">I3</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3</span>)</span>,<font color="Maroon" title="c1">n</font> ) &amp; ( <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 implies <font color="Maroon" title="c8">I4</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">I3</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4</span>)</span>,<font color="Maroon" title="c1">n</font> ) &amp; ( <font color="Olive" title="b1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Olive" title="b1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 &amp; <font color="Olive" title="b1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 3 &amp; <font color="Olive" title="b1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 4 implies <font color="Maroon" title="c8">I4</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">I3</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Olive" title="b1">i</font> ) ) ) )
 
<b>by </b><i><a class="txt" href="idea_1.html#E17:47"><i><font color="Green" title="E50">A13</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self" title="IDEA_1:def.11">Def11</a></i>;<br/>
<a NAME="E19:47"/><i><font color="Green" title="E52">A15</font></i>: 
 <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="c2">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">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/>
<i><font color="Green" title="E53">A16</font></i>:  <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="c2">m</font></span>)</span> = 
 <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="c5">I1</font></span>)</span>
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green" title="E45">A8</font></i></a>, <a class="ref" href="idea_1.html#D13" target="_self" title="IDEA_1:def.13">Def13</a></i>
<br/>.= 
 <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="c6">I2</font></span>)</span>
<b>by </b><i><a class="txt" href="idea_1.html#E11:47"><i><font color="Green" title="E46">A9</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self" title="IDEA_1:def.11">Def11</a></i>
<br/>.= 
 <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="c7">I3</font></span>)</span>
<b>by </b><i><a class="txt" href="idea_1.html#E14:47"><i><font color="Green" title="E48">A11</font></i></a>, <a class="ref" href="idea_1.html#D13" target="_self" title="IDEA_1:def.13">Def13</a></i>
<br/>.= 
 <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="c8">I4</font></span>)</span>
<b>by </b><i><a class="txt" href="idea_1.html#E17:47"><i><font color="Green" title="E50">A13</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self" title="IDEA_1:def.11">Def11</a></i>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c8">I4</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="E21:47"/>
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="c2">m</font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green" title="E38">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="E22:47"/><b>then </b><i><font color="Green" title="E54">A17</font></i>: 
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="c2">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="E23:47"/><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="c5">I1</font></span>)</span> &amp; 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="c6">I2</font></span>)</span> &amp; 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="c7">I3</font></span>)</span> &amp; 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="c8">I4</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green" title="E45">A8</font></i></a>, <a class="txt" href="idea_1.html#E12:47"><i><font color="Green" title="E47">A10</font></i></a>, <a class="txt" href="idea_1.html#E15:47"><i><font color="Green" title="E49">A12</font></i></a>, <a class="txt" href="idea_1.html#E18:47"><i><font color="Green" title="E51">A14</font></i></a>, <a class="ref" href="idea_1.html#D13" target="_self" title="IDEA_1:def.13">Def13</a></i>;<br/>
<a NAME="E24:47"/><b>then </b><i><font color="Green" title="E55">A18</font></i>: 
( 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="c5">I1</font> &amp; 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="c6">I2</font> &amp; 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="c7">I3</font> &amp; 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="c8">I4</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="E25:47"/><i><font color="Green" title="E56">A19</font></i>: 
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="c2">m</font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E22:47"><i><font color="Green" title="E54">A17</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E26:47"/>
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="c2">m</font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green" title="E38">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="E27:47"/><b>then </b><i><font color="Green" title="E57">A20</font></i>: 
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="c2">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="E28:47"/><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="c5">I1</font></span>)</span> &amp; 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="c6">I2</font></span>)</span> &amp; 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="c7">I3</font></span>)</span> &amp; 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="c8">I4</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green" title="E45">A8</font></i></a>, <a class="txt" href="idea_1.html#E12:47"><i><font color="Green" title="E47">A10</font></i></a>, <a class="txt" href="idea_1.html#E15:47"><i><font color="Green" title="E49">A12</font></i></a>, <a class="txt" href="idea_1.html#E18:47"><i><font color="Green" title="E51">A14</font></i></a>, <a class="ref" href="idea_1.html#D13" target="_self" title="IDEA_1:def.13">Def13</a></i>;<br/>
<a NAME="E29:47"/><b>then </b><i><font color="Green" title="E58">A21</font></i>: 
( 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="c5">I1</font> &amp; 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="c6">I2</font> &amp; 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="c7">I3</font> &amp; 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="c8">I4</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="E30:47"/><i><font color="Green" title="E59">A22</font></i>: 
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="c2">m</font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E27:47"><i><font color="Green" title="E57">A20</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E31:47"/>
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="c2">m</font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green" title="E38">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="E32:47"/><b>then </b><i><font color="Green" title="E60">A23</font></i>: 
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="c2">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="E33:47"/><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="c5">I1</font></span>)</span> &amp; 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="c6">I2</font></span>)</span> &amp; 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="c7">I3</font></span>)</span> &amp; 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="c8">I4</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green" title="E45">A8</font></i></a>, <a class="txt" href="idea_1.html#E12:47"><i><font color="Green" title="E47">A10</font></i></a>, <a class="txt" href="idea_1.html#E15:47"><i><font color="Green" title="E49">A12</font></i></a>, <a class="txt" href="idea_1.html#E18:47"><i><font color="Green" title="E51">A14</font></i></a>, <a class="ref" href="idea_1.html#D13" target="_self" title="IDEA_1:def.13">Def13</a></i>;<br/>
<a NAME="E34:47"/><b>then </b><i><font color="Green" title="E61">A24</font></i>: 
( 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="c5">I1</font> &amp; 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="c6">I2</font> &amp; 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="c7">I3</font> &amp; 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="c8">I4</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="E35:47"/><i><font color="Green" title="E62">A25</font></i>: 
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="c2">m</font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E32:47"><i><font color="Green" title="E60">A23</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E36:47"/><i><font color="Green" title="E63">A26</font></i>: 
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="c2">m</font></span>)</span>
 
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green" title="E38">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="E37:47"/><b>then </b>
( 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="c5">I1</font></span>)</span> &amp; 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="c6">I2</font></span>)</span> &amp; 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="c7">I3</font></span>)</span> &amp; 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="c8">I4</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green" title="E45">A8</font></i></a>, <a class="txt" href="idea_1.html#E12:47"><i><font color="Green" title="E47">A10</font></i></a>, <a class="txt" href="idea_1.html#E15:47"><i><font color="Green" title="E49">A12</font></i></a>, <a class="txt" href="idea_1.html#E18:47"><i><font color="Green" title="E51">A14</font></i></a>, <a class="ref" href="idea_1.html#D13" target="_self" title="IDEA_1:def.13">Def13</a></i>;<br/>
<a NAME="E38:47"/><b>then </b><i><font color="Green" title="E64">A27</font></i>: 
( 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="c5">I1</font> &amp; 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="c6">I2</font> &amp; 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="c7">I3</font> &amp; 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="c8">I4</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="E39:47"/><i><font color="Green" title="E65">A28</font></i>: 
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="c2">m</font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E36:47"><i><font color="Green" title="E63">A26</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>assume </b><a NAME="E1:47_2"/><i><font color="Green" title="E66">A29</font></i>: 
<font color="Maroon" title="c9">j</font> <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="c2">m</font></span>)</span>
 ;<br/><a NAME="E2:47_2"/><b>then </b><i><font color="Green" title="E67">A30</font></i>: 
<font color="Maroon" title="c9">j</font> <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="c5">I1</font></span>)</span>
 <b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green" title="E45">A8</font></i></a>, <a class="ref" href="idea_1.html#D13" target="_self" title="IDEA_1:def.13">Def13</a></i>;<br/><a NAME="E3:47_2"/><b>then </b><i><font color="Green" title="E68">A31</font></i>: 
<font color="Maroon" title="c9">j</font> <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="c6">I2</font></span>)</span>
 <b>by </b><i><a class="txt" href="idea_1.html#E11:47"><i><font color="Green" title="E46">A9</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self" title="IDEA_1:def.11">Def11</a></i>;<br/><a NAME="E4:47_2"/><b>then </b><i><font color="Green" title="E69">A32</font></i>: 
<font color="Maroon" title="c9">j</font> <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="c7">I3</font></span>)</span>
 <b>by </b><i><a class="txt" href="idea_1.html#E14:47"><i><font color="Green" title="E48">A11</font></i></a>, <a class="ref" href="idea_1.html#D13" target="_self" title="IDEA_1:def.13">Def13</a></i>;<br/><a NAME="E5:47_2"/><i><font color="Green" title="E70">A33</font></i>: 
<font color="Maroon" title="c9">j</font> <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="c5">I1</font>
 <b>by </b><i><a class="txt" href="idea_1.html#E2:47_2"><i><font color="Green" title="E67">A30</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E6:47_2"/><i><font color="Green" title="E71">A34</font></i>: 
<font color="Maroon" title="c9">j</font> <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="c6">I2</font>
 <b>by </b><i><a class="txt" href="idea_1.html#E3:47_2"><i><font color="Green" title="E68">A31</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E7:47_2"/><i><font color="Green" title="E72">A35</font></i>: 
<font color="Maroon" title="c9">j</font> <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="c7">I3</font>
 <b>by </b><i><a class="txt" href="idea_1.html#E4:47_2"><i><font color="Green" title="E69">A32</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E8:47_2"/><i><font color="Green" title="E73">A36</font></i>: 
<font color="Maroon" title="c9">j</font> <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="c2">m</font>
 <b>by </b><i><a class="txt" href="idea_1.html#E1:47_2"><i><font color="Green" title="E66">A29</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:47_2_1_1"/>
( <font color="Maroon" title="c9">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c9">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c9">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c9">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or ( <font color="Maroon" title="c9">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c9">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 &amp; <font color="Maroon" title="c9">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 3 &amp; <font color="Maroon" title="c9">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 4 ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_2_1_1_1"><b>suppose </b></a><a NAME="E1:47_2_1_1_1"/><i><font color="Green" title="E74">A37</font></i>: 
<font color="Maroon" title="c9">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c8">I4</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">j</font> = 
 <a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">I3</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E17:47"><i><font color="Green" title="E50">A13</font></i></a>, <a class="txt" href="idea_1.html#E24:47"><i><font color="Green" title="E55">A18</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self" title="IDEA_1:def.11">Def11</a></i>
<br/>.= 
 <a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">I2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E14:47"><i><font color="Green" title="E48">A11</font></i></a>, <a class="txt" href="idea_1.html#E24:47"><i><font color="Green" title="E55">A18</font></i></a>, <a class="txt" href="idea_1.html#E46"><i><font color="Green" title="E35">Lm5</font></i></a></i>
<br/>.= 
 <a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p1">(<span class="default"><a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">I1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1</span>)</span>,<font color="Maroon" title="c1">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E11:47"><i><font color="Green" title="E46">A9</font></i></a>, <a class="txt" href="idea_1.html#E24:47"><i><font color="Green" title="E55">A18</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self" title="IDEA_1:def.11">Def11</a></i>
<br/>.= 
 <a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p1">(<span class="default"><a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1</span>)</span>,<font color="Maroon" title="c1">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green" title="E45">A8</font></i></a>, <a class="txt" href="idea_1.html#E25:47"><i><font color="Green" title="E56">A19</font></i></a>, <a class="txt" href="idea_1.html#E46"><i><font color="Green" title="E35">Lm5</font></i></a></i>
<br/>.= 
 <a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1</span>)</span>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="idea_1.html#E6:47"><i><font color="Green" title="E43">A6</font></i></a>, <a class="ref" href="idea_1.html#T24" target="_self" title="IDEA_1:th.24">Th24</a></i>
<br/>.= 
 <a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> 1,<span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 1</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="idea_1.html#E2:47"><i><font color="Green" title="E39">A2</font></i></a>, <a class="ref" href="idea_1.html#D10" target="_self" title="IDEA_1:def.10">Def10</a></i>
<br/>.= 
<font color="Maroon" title="c2">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">j</font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="idea_1.html#E1:47_2_1_1_1"><i><font color="Green" title="E74">A37</font></i></a>, <a class="ref" href="idea_1.html#T23" target="_self" title="IDEA_1:th.23">Th23</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_2_1_1_2"><b>suppose </b></a><a NAME="E1:47_2_1_1_2"/><i><font color="Green" title="E74">A38</font></i>: 
<font color="Maroon" title="c9">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c8">I4</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">j</font> = 
 <a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">I3</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E17:47"><i><font color="Green" title="E50">A13</font></i></a>, <a class="txt" href="idea_1.html#E29:47"><i><font color="Green" title="E58">A21</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self" title="IDEA_1:def.11">Def11</a></i>
<br/>.= 
 <a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">I2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E14:47"><i><font color="Green" title="E48">A11</font></i></a>, <a class="txt" href="idea_1.html#E29:47"><i><font color="Green" title="E58">A21</font></i></a>, <a class="txt" href="idea_1.html#E44"><i><font color="Green" title="E33">Lm3</font></i></a></i>
<br/>.= 
 <a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p1">(<span class="default"><a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">I1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3</span>)</span>,<font color="Maroon" title="c1">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E11:47"><i><font color="Green" title="E46">A9</font></i></a>, <a class="txt" href="idea_1.html#E34:47"><i><font color="Green" title="E61">A24</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self" title="IDEA_1:def.11">Def11</a></i>
<br/>.= 
 <a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p1">(<span class="default"><a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3</span>)</span>,<font color="Maroon" title="c1">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green" title="E45">A8</font></i></a>, <a class="txt" href="idea_1.html#E35:47"><i><font color="Green" title="E62">A25</font></i></a>, <a class="txt" href="idea_1.html#E45"><i><font color="Green" title="E34">Lm4</font></i></a></i>
<br/>.= 
 <a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2</span>)</span>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="ref" href="idea_1.html#T15" target="_self" title="IDEA_1:th.15">Th15</a></i>
<br/>.= 
 <a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="idea_1.html#E3:47"><i><font color="Green" title="E40">A3</font></i></a>, <a class="ref" href="idea_1.html#T12" target="_self" title="IDEA_1:th.12">Th12</a></i>
<br/>.= 
<font color="Maroon" title="c2">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">j</font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="idea_1.html#E1:47_2_1_1_2"><i><font color="Green" title="E74">A38</font></i></a>, <a class="ref" href="idea_1.html#T14" target="_self" title="IDEA_1:th.14">Th14</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_2_1_1_3"><b>suppose </b></a><a NAME="E1:47_2_1_1_3"/><i><font color="Green" title="E74">A39</font></i>: 
<font color="Maroon" title="c9">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c8">I4</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">j</font> = 
 <a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">I3</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E17:47"><i><font color="Green" title="E50">A13</font></i></a>, <a class="txt" href="idea_1.html#E34:47"><i><font color="Green" title="E61">A24</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self" title="IDEA_1:def.11">Def11</a></i>
<br/>.= 
 <a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">I2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E14:47"><i><font color="Green" title="E48">A11</font></i></a>, <a class="txt" href="idea_1.html#E34:47"><i><font color="Green" title="E61">A24</font></i></a>, <a class="txt" href="idea_1.html#E45"><i><font color="Green" title="E34">Lm4</font></i></a></i>
<br/>.= 
 <a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p1">(<span class="default"><a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">I1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2</span>)</span>,<font color="Maroon" title="c1">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E11:47"><i><font color="Green" title="E46">A9</font></i></a>, <a class="txt" href="idea_1.html#E29:47"><i><font color="Green" title="E58">A21</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self" title="IDEA_1:def.11">Def11</a></i>
<br/>.= 
 <a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p1">(<span class="default"><a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2</span>)</span>,<font color="Maroon" title="c1">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green" title="E45">A8</font></i></a>, <a class="txt" href="idea_1.html#E30:47"><i><font color="Green" title="E59">A22</font></i></a>, <a class="txt" href="idea_1.html#E44"><i><font color="Green" title="E33">Lm3</font></i></a></i>
<br/>.= 
 <a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3</span>)</span>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="ref" href="idea_1.html#T15" target="_self" title="IDEA_1:th.15">Th15</a></i>
<br/>.= 
 <a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 3</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="idea_1.html#E4:47"><i><font color="Green" title="E41">A4</font></i></a>, <a class="ref" href="idea_1.html#T12" target="_self" title="IDEA_1:th.12">Th12</a></i>
<br/>.= 
<font color="Maroon" title="c2">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">j</font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="idea_1.html#E1:47_2_1_1_3"><i><font color="Green" title="E74">A39</font></i></a>, <a class="ref" href="idea_1.html#T14" target="_self" title="IDEA_1:th.14">Th14</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_2_1_1_4"><b>suppose </b></a><a NAME="E1:47_2_1_1_4"/><i><font color="Green" title="E74">A40</font></i>: 
<font color="Maroon" title="c9">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c8">I4</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">j</font> = 
 <a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">I3</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E17:47"><i><font color="Green" title="E50">A13</font></i></a>, <a class="txt" href="idea_1.html#E38:47"><i><font color="Green" title="E64">A27</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self" title="IDEA_1:def.11">Def11</a></i>
<br/>.= 
 <a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">I2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E14:47"><i><font color="Green" title="E48">A11</font></i></a>, <a class="txt" href="idea_1.html#E38:47"><i><font color="Green" title="E64">A27</font></i></a>, <a class="txt" href="idea_1.html#E46"><i><font color="Green" title="E35">Lm5</font></i></a></i>
<br/>.= 
 <a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p1">(<span class="default"><a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">I1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4</span>)</span>,<font color="Maroon" title="c1">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E11:47"><i><font color="Green" title="E46">A9</font></i></a>, <a class="txt" href="idea_1.html#E38:47"><i><font color="Green" title="E64">A27</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self" title="IDEA_1:def.11">Def11</a></i>
<br/>.= 
 <a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p1">(<span class="default"><a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4</span>)</span>,<font color="Maroon" title="c1">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green" title="E45">A8</font></i></a>, <a class="txt" href="idea_1.html#E39:47"><i><font color="Green" title="E65">A28</font></i></a>, <a class="txt" href="idea_1.html#E46"><i><font color="Green" title="E35">Lm5</font></i></a></i>
<br/>.= 
 <a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4</span>)</span>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="idea_1.html#E7:47"><i><font color="Green" title="E44">A7</font></i></a>, <a class="ref" href="idea_1.html#T24" target="_self" title="IDEA_1:th.24">Th24</a></i>
<br/>.= 
 <a href="idea_1.html#K9" title="IDEA_1:func.9">MUL_MOD</a> 1,<span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> 4</span>)</span>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="idea_1.html#E5:47"><i><font color="Green" title="E42">A5</font></i></a>, <a class="ref" href="idea_1.html#D10" target="_self" title="IDEA_1:def.10">Def10</a></i>
<br/>.= 
<font color="Maroon" title="c2">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">j</font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="idea_1.html#E1:47_2_1_1_4"><i><font color="Green" title="E74">A40</font></i></a>, <a class="ref" href="idea_1.html#T23" target="_self" title="IDEA_1:th.23">Th23</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_2_1_1_5"><b>suppose </b></a><a NAME="E1:47_2_1_1_5"/><i><font color="Green" title="E74">A41</font></i>: 
( <font color="Maroon" title="c9">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c9">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 &amp; <font color="Maroon" title="c9">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 3 &amp; <font color="Maroon" title="c9">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 4 )
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c8">I4</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">j</font> = 
<font color="Maroon" title="c7">I3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">j</font>
<b>by </b><i><a class="txt" href="idea_1.html#E17:47"><i><font color="Green" title="E50">A13</font></i></a>, <a class="txt" href="idea_1.html#E7:47_2"><i><font color="Green" title="E72">A35</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self" title="IDEA_1:def.11">Def11</a></i>
<br/>.= 
<font color="Maroon" title="c6">I2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">j</font>
<b>by </b><i><a class="txt" href="idea_1.html#E14:47"><i><font color="Green" title="E48">A11</font></i></a>, <a class="txt" href="idea_1.html#E6:47_2"><i><font color="Green" title="E71">A34</font></i></a>, <a class="txt" href="idea_1.html#E1:47_2_1_1_5"><i><font color="Green" title="E74">A41</font></i></a>, <a class="txt" href="idea_1.html#E46"><i><font color="Green" title="E35">Lm5</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c5">I1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">j</font>
<b>by </b><i><a class="txt" href="idea_1.html#E11:47"><i><font color="Green" title="E46">A9</font></i></a>, <a class="txt" href="idea_1.html#E5:47_2"><i><font color="Green" title="E70">A33</font></i></a>, <a class="txt" href="idea_1.html#E1:47_2_1_1_5"><i><font color="Green" title="E74">A41</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self" title="IDEA_1:def.11">Def11</a></i>
<br/>.= 
<font color="Maroon" title="c2">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">j</font>
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green" title="E45">A8</font></i></a>, <a class="txt" href="idea_1.html#E8:47_2"><i><font color="Green" title="E73">A36</font></i></a>, <a class="txt" href="idea_1.html#E1:47_2_1_1_5"><i><font color="Green" title="E74">A41</font></i></a>, <a class="txt" href="idea_1.html#E46"><i><font color="Green" title="E35">Lm5</font></i></a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E10:47_2"/>
<font color="Maroon" title="c8">I4</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">j</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E41:47"/>
 <a href="idea_1.html#K11" title="IDEA_1:func.11">IDEAoperationA</a> <span class="p1">(<span class="default"><a href="idea_1.html#K13" title="IDEA_1:func.13">IDEAoperationC</a> <span class="p2">(<span class="default"><a href="idea_1.html#K11" title="IDEA_1:func.11">IDEAoperationA</a> <span class="p3">(<span class="default"><a href="idea_1.html#K13" title="IDEA_1:func.13">IDEAoperationC</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span>,<font color="Maroon" title="c4">k2</font>,<font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font>
 <b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green" title="E45">A8</font></i></a>, <a class="txt" href="idea_1.html#E11:47"><i><font color="Green" title="E46">A9</font></i></a>, <a class="txt" href="idea_1.html#E14:47"><i><font color="Green" title="E48">A11</font></i></a>, <a class="txt" href="idea_1.html#E17:47"><i><font color="Green" title="E50">A13</font></i></a>, <a class="txt" href="idea_1.html#E19:47"><i><font color="Green" title="E52">A15</font></i></a>, <a class="txt" href="idea_1.html#E20:47"><i><font color="Green" title="E53">A16</font></i></a>, <a class="ref" href="finseq_1.html#T17" title="FINSEQ_1:th.17">FINSEQ_1:17</a></i>;<br/>


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