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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:47"/><i><font color="Green">E38</font></i>: 
( <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 is <a href="int_2.html#V1">prime</a> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 4 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 1 <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 2 <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 3 <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 4 <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 1 <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 2 <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 3 <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 4 <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>and </b><br/><a NAME="E2:47"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 1 <a href="hidden.html#R1">=</a>  <a href="idea_1.html#K10" target="_self">INV_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E3:47"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 2 <a href="hidden.html#R1">=</a>  <a href="idea_1.html#K6" target="_self">NEG_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E4:47"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 3 <a href="hidden.html#R1">=</a>  <a href="idea_1.html#K6" target="_self">NEG_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E5:47"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 4 <a href="hidden.html#R1">=</a>  <a href="idea_1.html#K10" target="_self">INV_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E6:47"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 1 <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green">E38</font></i></a>, <a class="txt" href="idea_1.html#E2:47"><i><font color="Green">E39</font></i></a>, <a class="ref" href="idea_1.html#D10" target="_self">Def10</a></i>;<br/>
<a NAME="E7:47"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 4 <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green">E38</font></i></a>, <a class="txt" href="idea_1.html#E5:47"><i><font color="Green">E42</font></i></a>, <a class="ref" href="idea_1.html#D10" target="_self">Def10</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E9:47"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="idea_1.html#K13" target="_self">IDEAoperationC</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E11:47"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="idea_1.html#K11" target="_self">IDEAoperationA</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 ;<br/>
<a NAME="E12:47"/><i><font color="Green">E47</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font> holds <br/>( ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1 implies <font color="Maroon">c<sub>6</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,<font color="Maroon">c<sub>1</sub></font> ) &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 2 implies <font color="Maroon">c<sub>6</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,<font color="Maroon">c<sub>1</sub></font> ) &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 3 implies <font color="Maroon">c<sub>6</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,<font color="Maroon">c<sub>1</sub></font> ) &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 4 implies <font color="Maroon">c<sub>6</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,<font color="Maroon">c<sub>1</sub></font> ) &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 3 &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 4 implies <font color="Maroon">c<sub>6</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> ) ) ) )
 
<b>by </b><i><a class="txt" href="idea_1.html#E11:47"><i><font color="Green">E46</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self">Def11</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E14:47"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="idea_1.html#K13" target="_self">IDEAoperationC</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>
<a NAME="E15:47"/><i><font color="Green">E49</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> holds <br/>( ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 2 implies <font color="Maroon">c<sub>7</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="wsierp_1.html#K3">.</a> 3 ) &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 3 implies <font color="Maroon">c<sub>7</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="wsierp_1.html#K3">.</a> 2 ) &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 3 implies <font color="Maroon">c<sub>7</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> ) ) ) )
 
<b>by </b><i><a class="txt" href="idea_1.html#E14:47"><i><font color="Green">E48</font></i></a>, <a class="ref" href="idea_1.html#D13" target="_self">Def13</a>, <a class="txt" href="idea_1.html#E44"><i><font color="Green">Lemma33</font></i></a>, <a class="txt" href="idea_1.html#E45"><i><font color="Green">Lemma34</font></i></a>, <a class="txt" href="idea_1.html#E46"><i><font color="Green">Lemma35</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E17:47"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="idea_1.html#K11" target="_self">IDEAoperationA</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 ;<br/>
<a NAME="E18:47"/><i><font color="Green">E51</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> holds <br/>( ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1 implies <font color="Maroon">c<sub>8</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,<font color="Maroon">c<sub>1</sub></font> ) &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 2 implies <font color="Maroon">c<sub>8</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,<font color="Maroon">c<sub>1</sub></font> ) &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 3 implies <font color="Maroon">c<sub>8</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,<font color="Maroon">c<sub>1</sub></font> ) &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 4 implies <font color="Maroon">c<sub>8</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,<font color="Maroon">c<sub>1</sub></font> ) &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 3 &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 4 implies <font color="Maroon">c<sub>8</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> ) ) ) )
 
<b>by </b><i><a class="txt" href="idea_1.html#E17:47"><i><font color="Green">E50</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self">Def11</a></i>;<br/>
<a NAME="E19:47"/><i><font color="Green">E52</font></i>: 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<i><font color="Green">E53</font></i>:  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green">E45</font></i></a>, <a class="ref" href="idea_1.html#D13" target="_self">Def13</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="idea_1.html#E11:47"><i><font color="Green">E46</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self">Def11</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="idea_1.html#E14:47"><i><font color="Green">E48</font></i></a>, <a class="ref" href="idea_1.html#D13" target="_self">Def13</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="idea_1.html#E17:47"><i><font color="Green">E50</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self">Def11</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
;<br/>
<a NAME="E21:47"/>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green">E38</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E22:47"/><b>then </b><i><font color="Green">E54</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E23:47"/><b>then </b>
( 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> &amp; 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> &amp; 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green">E45</font></i></a>, <a class="txt" href="idea_1.html#E12:47"><i><font color="Green">E47</font></i></a>, <a class="txt" href="idea_1.html#E15:47"><i><font color="Green">E49</font></i></a>, <a class="txt" href="idea_1.html#E18:47"><i><font color="Green">E51</font></i></a>, <a class="ref" href="idea_1.html#D13" target="_self">Def13</a></i>;<br/>
<a NAME="E24:47"/><b>then </b><i><font color="Green">E55</font></i>: 
( 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font> &amp; 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> &amp; 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> &amp; 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E25:47"/><i><font color="Green">E56</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E22:47"><i><font color="Green">E54</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E26:47"/>
2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green">E38</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E27:47"/><b>then </b><i><font color="Green">E57</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E28:47"/><b>then </b>
( 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green">E45</font></i></a>, <a class="txt" href="idea_1.html#E12:47"><i><font color="Green">E47</font></i></a>, <a class="txt" href="idea_1.html#E15:47"><i><font color="Green">E49</font></i></a>, <a class="txt" href="idea_1.html#E18:47"><i><font color="Green">E51</font></i></a>, <a class="ref" href="idea_1.html#D13" target="_self">Def13</a></i>;<br/>
<a NAME="E29:47"/><b>then </b><i><font color="Green">E58</font></i>: 
( 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E30:47"/><i><font color="Green">E59</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E27:47"><i><font color="Green">E57</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E31:47"/>
3 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green">E38</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E32:47"/><b>then </b><i><font color="Green">E60</font></i>: 
3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E33:47"/><b>then </b>
( 3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> &amp; 3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; 3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> &amp; 3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green">E45</font></i></a>, <a class="txt" href="idea_1.html#E12:47"><i><font color="Green">E47</font></i></a>, <a class="txt" href="idea_1.html#E15:47"><i><font color="Green">E49</font></i></a>, <a class="txt" href="idea_1.html#E18:47"><i><font color="Green">E51</font></i></a>, <a class="ref" href="idea_1.html#D13" target="_self">Def13</a></i>;<br/>
<a NAME="E34:47"/><b>then </b><i><font color="Green">E61</font></i>: 
( 3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font> &amp; 3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> &amp; 3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> &amp; 3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E35:47"/><i><font color="Green">E62</font></i>: 
3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E32:47"><i><font color="Green">E60</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E36:47"/><i><font color="Green">E63</font></i>: 
4 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green">E38</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E37:47"/><b>then </b>
( 4 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> &amp; 4 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; 4 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> &amp; 4 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green">E45</font></i></a>, <a class="txt" href="idea_1.html#E12:47"><i><font color="Green">E47</font></i></a>, <a class="txt" href="idea_1.html#E15:47"><i><font color="Green">E49</font></i></a>, <a class="txt" href="idea_1.html#E18:47"><i><font color="Green">E51</font></i></a>, <a class="ref" href="idea_1.html#D13" target="_self">Def13</a></i>;<br/>
<a NAME="E38:47"/><b>then </b><i><font color="Green">E64</font></i>: 
( 4 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font> &amp; 4 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> &amp; 4 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> &amp; 4 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E39:47"/><i><font color="Green">E65</font></i>: 
4 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E36:47"><i><font color="Green">E63</font></i></a>, <a class="ref" href="finseq_1.html#D3">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">c<sub>9</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:47_2"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/><a NAME="E2:47_2"/><b>then </b><i><font color="Green">E67</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green">E45</font></i></a>, <a class="ref" href="idea_1.html#D13" target="_self">Def13</a></i>;<br/><a NAME="E3:47_2"/><b>then </b><i><font color="Green">E68</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="idea_1.html#E11:47"><i><font color="Green">E46</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self">Def11</a></i>;<br/><a NAME="E4:47_2"/><b>then </b><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="idea_1.html#E14:47"><i><font color="Green">E48</font></i></a>, <a class="ref" href="idea_1.html#D13" target="_self">Def13</a></i>;<br/><a NAME="E5:47_2"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="idea_1.html#E2:47_2"><i><font color="Green">E67</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E6:47_2"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="idea_1.html#E3:47_2"><i><font color="Green">E68</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E7:47_2"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="idea_1.html#E4:47_2"><i><font color="Green">E69</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E8:47_2"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="idea_1.html#E1:47_2"><i><font color="Green">E66</font></i></a>, <a class="ref" href="finseq_1.html#D3">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">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> 3 or <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> 4 or ( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 3 &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&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">E74</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>hence </b><font color="Maroon">c<sub>8</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font> = 
 <a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E17:47"><i><font color="Green">E50</font></i></a>, <a class="txt" href="idea_1.html#E24:47"><i><font color="Green">E55</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self">Def11</a></i>
<br/>.= 
 <a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E14:47"><i><font color="Green">E48</font></i></a>, <a class="txt" href="idea_1.html#E24:47"><i><font color="Green">E55</font></i></a>, <a class="txt" href="idea_1.html#E46"><i><font color="Green">Lemma35</font></i></a></i>
<br/>.= 
 <a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p1">(<span class="default"><a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E11:47"><i><font color="Green">E46</font></i></a>, <a class="txt" href="idea_1.html#E24:47"><i><font color="Green">E55</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self">Def11</a></i>
<br/>.= 
 <a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p1">(<span class="default"><a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green">E45</font></i></a>, <a class="txt" href="idea_1.html#E25:47"><i><font color="Green">E56</font></i></a>, <a class="txt" href="idea_1.html#E46"><i><font color="Green">Lemma35</font></i></a></i>
<br/>.= 
 <a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green">E38</font></i></a>, <a class="txt" href="idea_1.html#E6:47"><i><font color="Green">E43</font></i></a>, <a class="ref" href="idea_1.html#T24" target="_self">Th24</a></i>
<br/>.= 
 <a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,1,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green">E38</font></i></a>, <a class="txt" href="idea_1.html#E2:47"><i><font color="Green">E39</font></i></a>, <a class="ref" href="idea_1.html#D10" target="_self">Def10</a></i>
<br/>.= 
 <a href="idea_1.html#K9" target="_self">MUL_MOD</a> 1,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 1</span>)</span>,<font color="Maroon">c<sub>1</sub></font>

<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green">E38</font></i></a>, <a class="txt" href="idea_1.html#E1:47_2_1_1_1"><i><font color="Green">E74</font></i></a>, <a class="ref" href="idea_1.html#T23" target="_self">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">E74</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><b>hence </b><font color="Maroon">c<sub>8</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font> = 
 <a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E17:47"><i><font color="Green">E50</font></i></a>, <a class="txt" href="idea_1.html#E29:47"><i><font color="Green">E58</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self">Def11</a></i>
<br/>.= 
 <a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E14:47"><i><font color="Green">E48</font></i></a>, <a class="txt" href="idea_1.html#E29:47"><i><font color="Green">E58</font></i></a>, <a class="txt" href="idea_1.html#E44"><i><font color="Green">Lemma33</font></i></a></i>
<br/>.= 
 <a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p1">(<span class="default"><a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E11:47"><i><font color="Green">E46</font></i></a>, <a class="txt" href="idea_1.html#E34:47"><i><font color="Green">E61</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self">Def11</a></i>
<br/>.= 
 <a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p1">(<span class="default"><a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green">E45</font></i></a>, <a class="txt" href="idea_1.html#E35:47"><i><font color="Green">E62</font></i></a>, <a class="txt" href="idea_1.html#E45"><i><font color="Green">Lemma34</font></i></a></i>
<br/>.= 
 <a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="idea_1.html#T15" target="_self">Th15</a></i>
<br/>.= 
 <a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,0,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green">E38</font></i></a>, <a class="txt" href="idea_1.html#E3:47"><i><font color="Green">E40</font></i></a>, <a class="ref" href="idea_1.html#T12" target="_self">Th12</a></i>
<br/>.= 
 <a href="idea_1.html#K4" target="_self">ADD_MOD</a> 0,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,<font color="Maroon">c<sub>1</sub></font>

<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green">E38</font></i></a>, <a class="txt" href="idea_1.html#E1:47_2_1_1_2"><i><font color="Green">E74</font></i></a>, <a class="ref" href="idea_1.html#T14" target="_self">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">E74</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><b>hence </b><font color="Maroon">c<sub>8</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font> = 
 <a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E17:47"><i><font color="Green">E50</font></i></a>, <a class="txt" href="idea_1.html#E34:47"><i><font color="Green">E61</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self">Def11</a></i>
<br/>.= 
 <a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E14:47"><i><font color="Green">E48</font></i></a>, <a class="txt" href="idea_1.html#E34:47"><i><font color="Green">E61</font></i></a>, <a class="txt" href="idea_1.html#E45"><i><font color="Green">Lemma34</font></i></a></i>
<br/>.= 
 <a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p1">(<span class="default"><a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E11:47"><i><font color="Green">E46</font></i></a>, <a class="txt" href="idea_1.html#E29:47"><i><font color="Green">E58</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self">Def11</a></i>
<br/>.= 
 <a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p1">(<span class="default"><a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green">E45</font></i></a>, <a class="txt" href="idea_1.html#E30:47"><i><font color="Green">E59</font></i></a>, <a class="txt" href="idea_1.html#E44"><i><font color="Green">Lemma33</font></i></a></i>
<br/>.= 
 <a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="idea_1.html#T15" target="_self">Th15</a></i>
<br/>.= 
 <a href="idea_1.html#K4" target="_self">ADD_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,0,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green">E38</font></i></a>, <a class="txt" href="idea_1.html#E4:47"><i><font color="Green">E41</font></i></a>, <a class="ref" href="idea_1.html#T12" target="_self">Th12</a></i>
<br/>.= 
 <a href="idea_1.html#K4" target="_self">ADD_MOD</a> 0,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 3</span>)</span>,<font color="Maroon">c<sub>1</sub></font>

<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green">E38</font></i></a>, <a class="txt" href="idea_1.html#E1:47_2_1_1_3"><i><font color="Green">E74</font></i></a>, <a class="ref" href="idea_1.html#T14" target="_self">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">E74</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> 4
 ;<br/><div class="add"><b>hence </b><font color="Maroon">c<sub>8</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font> = 
 <a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E17:47"><i><font color="Green">E50</font></i></a>, <a class="txt" href="idea_1.html#E38:47"><i><font color="Green">E64</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self">Def11</a></i>
<br/>.= 
 <a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E14:47"><i><font color="Green">E48</font></i></a>, <a class="txt" href="idea_1.html#E38:47"><i><font color="Green">E64</font></i></a>, <a class="txt" href="idea_1.html#E46"><i><font color="Green">Lemma35</font></i></a></i>
<br/>.= 
 <a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p1">(<span class="default"><a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E11:47"><i><font color="Green">E46</font></i></a>, <a class="txt" href="idea_1.html#E38:47"><i><font color="Green">E64</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self">Def11</a></i>
<br/>.= 
 <a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p1">(<span class="default"><a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green">E45</font></i></a>, <a class="txt" href="idea_1.html#E39:47"><i><font color="Green">E65</font></i></a>, <a class="txt" href="idea_1.html#E46"><i><font color="Green">Lemma35</font></i></a></i>
<br/>.= 
 <a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green">E38</font></i></a>, <a class="txt" href="idea_1.html#E7:47"><i><font color="Green">E44</font></i></a>, <a class="ref" href="idea_1.html#T24" target="_self">Th24</a></i>
<br/>.= 
 <a href="idea_1.html#K9" target="_self">MUL_MOD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,1,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green">E38</font></i></a>, <a class="txt" href="idea_1.html#E5:47"><i><font color="Green">E42</font></i></a>, <a class="ref" href="idea_1.html#D10" target="_self">Def10</a></i>
<br/>.= 
 <a href="idea_1.html#K9" target="_self">MUL_MOD</a> 1,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> 4</span>)</span>,<font color="Maroon">c<sub>1</sub></font>

<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:47"><i><font color="Green">E38</font></i></a>, <a class="txt" href="idea_1.html#E1:47_2_1_1_4"><i><font color="Green">E74</font></i></a>, <a class="ref" href="idea_1.html#T23" target="_self">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">E74</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 3 &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 4 )
 ;<br/><div class="add"><b>hence </b><font color="Maroon">c<sub>8</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font> = 
<font color="Maroon">c<sub>7</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E17:47"><i><font color="Green">E50</font></i></a>, <a class="txt" href="idea_1.html#E7:47_2"><i><font color="Green">E72</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self">Def11</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E14:47"><i><font color="Green">E48</font></i></a>, <a class="txt" href="idea_1.html#E6:47_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="idea_1.html#E1:47_2_1_1_5"><i><font color="Green">E74</font></i></a>, <a class="txt" href="idea_1.html#E46"><i><font color="Green">Lemma35</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E11:47"><i><font color="Green">E46</font></i></a>, <a class="txt" href="idea_1.html#E5:47_2"><i><font color="Green">E70</font></i></a>, <a class="txt" href="idea_1.html#E1:47_2_1_1_5"><i><font color="Green">E74</font></i></a>, <a class="ref" href="idea_1.html#D11" target="_self">Def11</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green">E45</font></i></a>, <a class="txt" href="idea_1.html#E8:47_2"><i><font color="Green">E73</font></i></a>, <a class="txt" href="idea_1.html#E1:47_2_1_1_5"><i><font color="Green">E74</font></i></a>, <a class="txt" href="idea_1.html#E46"><i><font color="Green">Lemma35</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">c<sub>8</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E41:47"/>
 <a href="idea_1.html#K11" target="_self">IDEAoperationA</a> <span class="p1">(<span class="default"><a href="idea_1.html#K13" target="_self">IDEAoperationC</a> <span class="p2">(<span class="default"><a href="idea_1.html#K11" target="_self">IDEAoperationA</a> <span class="p3">(<span class="default"><a href="idea_1.html#K13" target="_self">IDEAoperationC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="idea_1.html#E9:47"><i><font color="Green">E45</font></i></a>, <a class="txt" href="idea_1.html#E11:47"><i><font color="Green">E46</font></i></a>, <a class="txt" href="idea_1.html#E14:47"><i><font color="Green">E48</font></i></a>, <a class="txt" href="idea_1.html#E17:47"><i><font color="Green">E50</font></i></a>, <a class="txt" href="idea_1.html#E19:47"><i><font color="Green">E52</font></i></a>, <a class="txt" href="idea_1.html#E20:47"><i><font color="Green">E53</font></i></a>, <a class="ref" href="finseq_1.html#T17">FINSEQ_1:17</a></i>;<br/>


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