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<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K3">*</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>





<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>3</sub></font> as    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>2</sub></font> <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="ref" href="polynom1.html#T35" target="_self">Th35</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>thus </b><a NAME="E2:61"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>5</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> as    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="finseq_2.html#T36">FINSEQ_2:36</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1"><b>now </b></a><div class="add"><a NAME="E1:61_1"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="finseq_2.html#T37">FINSEQ_2:37</a></i>;<br/><b>hence </b><a NAME="E2:61_1"/><i><font color="Green">E37</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</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_3.html#T31">FINSEQ_3:31</a></i>;<br/><a NAME="E3:61_1"/><i><font color="Green">E38</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5" target="_self">Card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="card_3.html#D2">CARD_3:def 2</a></i>;<br/><i><font color="Green">E39</font></i>:  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#D24">PBOOLE:def 24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>

;<br/><a NAME="E5:61_1"/><b>then </b><i><font color="Green">E40</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5" target="_self">Card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="card_3.html#D2">CARD_3:def 2</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>9</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:61_1_2"/><i><font color="Green">E41</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>3</sub></font>
 ;<br/><b>then </b><i><font color="Green">E42</font></i>: <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E4:61_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="pboole.html#D24">PBOOLE:def 24</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E1:61_1_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
;<br/><a NAME="E3:61_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K3">*</a> 
 <b>by </b><i><a class="txt" href="polynom1.html#E1:61_1_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="finseq_2.html#T13">FINSEQ_2:13</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> as    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="polynom1.html#K5" target="_self">Card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font> = 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="polynom1.html#E1:61_1_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="card_3.html#D2">CARD_3:def 2</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E2:61_1_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="finseq_2.html#T37">FINSEQ_2:37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom1.html#K5" target="_self">Card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="polynom1.html#E4:61_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="polynom1.html#E1:61_1_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="card_3.html#D2">CARD_3:def 2</a></i>
;<br/></div><b>end;</b></div><a NAME="E7:61_1"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="polynom1.html#K5" target="_self">Card</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K5" target="_self">Card</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E3:61_1"><i><font color="Green">E38</font></i></a>, <a class="txt" href="polynom1.html#E5:61_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E8:61_1"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T31" target="_self">Th31</a></i>;<br/><b>hence </b><a NAME="E9:61_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><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="E10:61_1"/><i><font color="Green">E42</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> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E12:61_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E13:61_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E14:61_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K8">Sum</a> <span class="p2">(<span class="default"><a href="polynom1.html#K5" target="_self">Card</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>11</sub></font>
 <b>and </b><br/><a NAME="E15:61_1"/><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="polynom1.html#T32" target="_self">Th32</a></i>;<br/><a NAME="E16:61_1"/><i><font color="Green">E47</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><a NAME="E17:61_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K3">*</a> 
 <b>by </b><i><a class="txt" href="polynom1.html#E12:61_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="finseq_2.html#T13">FINSEQ_2:13</a></i>;<br/><a NAME="E18:61_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> is    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/><a NAME="E19:61_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E16:61_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/><a NAME="E20:61_1"/><b>then </b><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom1.html#E13:61_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/><i><font color="Green">E49</font></i>: <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E4:61_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="polynom1.html#E12:61_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="pboole.html#D24">PBOOLE:def 24</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E12:61_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
;<br/><a NAME="E22:61_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K3">*</a> 
 <b>by </b><i><a class="txt" href="polynom1.html#E12:61_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="finseq_2.html#T13">FINSEQ_2:13</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> as    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/><a NAME="E24:61_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom1.html#E21:61_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="finseq_2.html#T37">FINSEQ_2:37</a></i>;<br/><a NAME="E25:61_1"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom1.html#E13:61_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/> <a href="polynom1.html#K5" target="_self">Card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="finseq_1.html#K17">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> = 
 <a href="card_3.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D15">FINSEQ_1:def 15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom1.html#K5" target="_self">Card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="rfunct_3.html#K23">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E7:61_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="polynom1.html#T11" target="_self">Th11</a></i>
<br/>.= 
 <a href="card_3.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T11" target="_self">Th11</a></i>
<br/>.= 
 <a href="polynom1.html#K5" target="_self">Card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K17">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D15">FINSEQ_1:def 15</a></i>
;<br/><b>then </b><span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="polynom1.html#E4:61_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="polynom1.html#E12:61_1"><i><font color="Green">E43</font></i></a>, <a class="txt" href="polynom1.html#E14:61_1"><i><font color="Green">E45</font></i></a>, <a class="txt" href="polynom1.html#E25:61_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="polynom1.html#T33" target="_self">Th33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="polynom1.html#E4:61_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="polynom1.html#E12:61_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="pboole.html#D24">PBOOLE:def 24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="polynom1.html#E12:61_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E20:61_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>
;<br/><b>hence </b><a NAME="E28:61_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E2:61_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="polynom1.html#E10:61_1"><i><font color="Green">E42</font></i></a>, <a class="txt" href="polynom1.html#E15:61_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:61"/>
<font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T17">FINSEQ_1:17</a></i>;<br/>


</div>
