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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><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 <span class="p1">(<span class="default">3 <a href="finseq_2.html#K4">-tuples_on</a> <span class="p2">(<span class="default"><a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="finseq_2.html#K3">*</a> ;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:158"/><i><font color="Green">E90</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#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E2:158"/><i><font color="Green">E91</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>4</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#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E3:158"/><i><font color="Green">E92</font></i>: 
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>3</sub></font> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 <b>and </b><br/><a NAME="E4:158"/><i><font color="Green">E93</font></i>: 
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>4</sub></font> holds <br/><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</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#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="dtconstr.html#K15">FlattenSeq</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>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="158_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:158_1_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</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>9</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:158_1_1"/><i><font color="Green">E94</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> &amp; <font color="Maroon">c<sub>8</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="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>9</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="polynom1.html#E3:158_1_1"><i><font color="Green">E94</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E6:158_1_1"/><i><font color="Green">E95</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> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E7:158_1_1"/><i><font color="Green">E96</font></i>: 
<font color="Maroon">c<sub>12</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>11</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E8:158_1_1"/>
<font color="Maroon">c<sub>10</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>11</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>12</sub></font>
 <b>and </b><br/><a NAME="E9:158_1_1"/><i><font color="Green">E97</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>11</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</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>10</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E3:158_1_1"><i><font color="Green">E94</font></i></a>, <a class="ref" href="polynom1.html#T32" target="_self">Th32</a></i>;<br/><b>set </b><font color="Maroon">c<sub>13</sub></font> =  <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>;<br/><a NAME="E10:158_1_1"/><i><font color="Green">E98</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <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="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom1.html#E3:158"><i><font color="Green">E92</font></i></a>, <a class="txt" href="polynom1.html#E6:158_1_1"><i><font color="Green">E95</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>15</sub></font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E12:158_1_1"/><i><font color="Green">E99</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E13:158_1_1"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>14</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E1:158"><i><font color="Green">E90</font></i></a>, <a class="txt" href="polynom1.html#E6:158_1_1"><i><font color="Green">E95</font></i></a>, <a class="ref" href="polynom1.html#T72" target="_self">Th72</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>15</sub></font> as    <a href="polynom1.html#M1" target="_self">Element</a> of  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="polynom1.html#D14" target="_self">Def14</a></i>;<br/><a NAME="E15:158_1_1"/><i><font color="Green">E101</font></i>: 
( <font color="Maroon">c<sub>16</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>15</sub></font> )
 ;<br/><a NAME="E16:158_1_1"/><b>then </b><i><font color="Green">E102</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E12:158_1_1"><i><font color="Green">E99</font></i></a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/><a NAME="E17:158_1_1"/><i><font color="Green">E103</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E12:158_1_1"><i><font color="Green">E99</font></i></a>, <a class="txt" href="polynom1.html#E15:158_1_1"><i><font color="Green">E101</font></i></a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/><i><font color="Green">E104</font></i>:  <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>11</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></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> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E10:158_1_1"><i><font color="Green">E98</font></i></a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></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> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span>

;<br/><b>then consider </b><font color="Maroon">c<sub>18</sub></font>, <font color="Maroon">c<sub>19</sub></font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E20:158_1_1"/><i><font color="Green">E105</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E21:158_1_1"/><i><font color="Green">E106</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E7:158_1_1"><i><font color="Green">E96</font></i></a>, <a class="txt" href="polynom1.html#E16:158_1_1"><i><font color="Green">E102</font></i></a>, <a class="ref" href="polynom1.html#T72" target="_self">Th72</a></i>;<br/><a NAME="E22:158_1_1"/><i><font color="Green">E107</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E23:158_1_1"/><i><font color="Green">E108</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E7:158_1_1"><i><font color="Green">E96</font></i></a>, <a class="txt" href="polynom1.html#E18:158_1_1"><i><font color="Green">E104</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/><a NAME="E24:158_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="polynom1.html#E7:158_1_1"><i><font color="Green">E96</font></i></a>, <a class="txt" href="polynom1.html#E18:158_1_1"><i><font color="Green">E104</font></i></a>, <a class="txt" href="polynom1.html#E22:158_1_1"><i><font color="Green">E107</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/><b>then </b><i><font color="Green">E109</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>11</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> = 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>15</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span>
<b>by </b><i><a class="txt" href="polynom1.html#E7:158_1_1"><i><font color="Green">E96</font></i></a>, <a class="txt" href="polynom1.html#E10:158_1_1"><i><font color="Green">E98</font></i></a>, <a class="txt" href="polynom1.html#E17:158_1_1"><i><font color="Green">E103</font></i></a>, <a class="txt" href="polynom1.html#E20:158_1_1"><i><font color="Green">E105</font></i></a>, <a class="txt" href="polynom1.html#E23:158_1_1"><i><font color="Green">E108</font></i></a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>15</sub></font></span><a href="finseq_1.html#K11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
;<br/><a NAME="E26:158_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom1.html#E13:158_1_1"><i><font color="Green">E100</font></i></a>, <a class="txt" href="polynom1.html#E21:158_1_1"><i><font color="Green">E106</font></i></a>, <a class="ref" href="polynom1.html#T39" target="_self">Th39</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>20</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E28:158_1_1"/><i><font color="Green">E110</font></i>: 
<font color="Maroon">c<sub>20</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="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E29:158_1_1"/><i><font color="Green">E111</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>18</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="polynom1.html#T73" target="_self">Th73</a></i>;<br/><b>set </b><font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>19</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>15</sub></font>;<br/><b>consider </b><font color="Maroon">c<sub>22</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E31:158_1_1"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">c<sub>22</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="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E32:158_1_1"/><i><font color="Green">E113</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>15</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="polynom1.html#T73" target="_self">Th73</a></i>;<br/><b>set </b><font color="Maroon">c<sub>23</sub></font> =  <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span>;<br/><a NAME="E33:158_1_1"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>20</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#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom1.html#E2:158"><i><font color="Green">E91</font></i></a>, <a class="txt" href="polynom1.html#E4:158"><i><font color="Green">E93</font></i></a>, <a class="txt" href="polynom1.html#E28:158_1_1"><i><font color="Green">E110</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>24</sub></font> = <font color="Maroon">c<sub>18</sub></font>, <font color="Maroon">c<sub>25</sub></font> = <font color="Maroon">c<sub>19</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>15</sub></font> as    <a href="polynom1.html#M1" target="_self">Element</a> of  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="polynom1.html#D14" target="_self">Def14</a></i>;<br/><a NAME="E35:158_1_1"/><i><font color="Green">E115</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>25</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="polynom1.html#E29:158_1_1"><i><font color="Green">E111</font></i></a></i>;<br/><a NAME="E36:158_1_1"/><b>then </b><i><font color="Green">E116</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/><a NAME="E37:158_1_1"/><i><font color="Green">E117</font></i>: 
 <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom1.html#E35:158_1_1"><i><font color="Green">E115</font></i></a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/><i><font color="Green">E118</font></i>:  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></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> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E33:158_1_1"><i><font color="Green">E114</font></i></a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></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> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></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> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>

;<br/><a NAME="E39:158_1_1"/><b>then </b><i><font color="Green">E119</font></i>: 
<font color="Maroon">c<sub>22</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>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom1.html#E31:158_1_1"><i><font color="Green">E112</font></i></a>, <a class="txt" href="polynom1.html#E35:158_1_1"><i><font color="Green">E115</font></i></a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/><a NAME="E40:158_1_1"/><b>then </b><i><font color="Green">E120</font></i>: 
<font color="Maroon">c<sub>22</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> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom1.html#E38:158_1_1"><i><font color="Green">E118</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E41:158_1_1"/><i><font color="Green">E121</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>22</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E31:158_1_1"><i><font color="Green">E112</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/><i><font color="Green">E122</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>22</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#K3">len</a> <span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E33:158_1_1"><i><font color="Green">E114</font></i></a>, <a class="txt" href="polynom1.html#E39:158_1_1"><i><font color="Green">E119</font></i></a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>18</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>15</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="txt" href="polynom1.html#E32:158_1_1"><i><font color="Green">E113</font></i></a>, <a class="txt" href="polynom1.html#E36:158_1_1"><i><font color="Green">E116</font></i></a>, <a class="txt" href="polynom1.html#E37:158_1_1"><i><font color="Green">E117</font></i></a>, <a class="txt" href="polynom1.html#E40:158_1_1"><i><font color="Green">E120</font></i></a>, <a class="txt" href="polynom1.html#E41:158_1_1"><i><font color="Green">E121</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>15</sub></font></span><a href="finseq_1.html#K11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
;<br/><b>set </b><font color="Maroon">c<sub>26</sub></font> = <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>4</sub></font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>20</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>22</sub></font>;<br/><a NAME="E43:158_1_1"/><i><font color="Green">E123</font></i>: 
<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>4</sub></font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>20</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>22</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>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom1.html#E2:158"><i><font color="Green">E91</font></i></a>, <a class="txt" href="polynom1.html#E28:158_1_1"><i><font color="Green">E110</font></i></a>, <a class="txt" href="polynom1.html#E39:158_1_1"><i><font color="Green">E119</font></i></a>, <a class="ref" href="polynom1.html#T33" target="_self">Th33</a></i>;<br/><a NAME="E44:158_1_1"/>
<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="wsierp_1.html#K8">Sum</a> <span class="p3">(<span class="default"><a href="polynom1.html#K5" target="_self">Card</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_1.html#K17">|</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>20</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>22</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>22</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E2:158"><i><font color="Green">E91</font></i></a>, <a class="txt" href="polynom1.html#E28:158_1_1"><i><font color="Green">E110</font></i></a>, <a class="txt" href="polynom1.html#E39:158_1_1"><i><font color="Green">E119</font></i></a>, <a class="ref" href="polynom1.html#T33" target="_self">Th33</a></i>;<br/><b>hence </b><a NAME="E45:158_1_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom1.html#E3:158_1_1"><i><font color="Green">E94</font></i></a>, <a class="txt" href="polynom1.html#E9:158_1_1"><i><font color="Green">E97</font></i></a>, <a class="txt" href="polynom1.html#E25:158_1_1"><i><font color="Green">E109</font></i></a>, <a class="txt" href="polynom1.html#E42:158_1_1"><i><font color="Green">E122</font></i></a>, <a class="txt" href="polynom1.html#E43:158_1_1"><i><font color="Green">E123</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:158_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>9</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:158_1"/><i><font color="Green">E94</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>4</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>8</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>4</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="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>9</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="polynom1.html#E4:158_1"><i><font color="Green">E94</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E7:158_1"/><i><font color="Green">E95</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> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E8:158_1"/><i><font color="Green">E96</font></i>: 
<font color="Maroon">c<sub>12</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>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E9:158_1"/>
<font color="Maroon">c<sub>10</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>4</sub></font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>11</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>12</sub></font>
 <b>and </b><br/><a NAME="E10:158_1"/><i><font color="Green">E97</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</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>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E4:158_1"><i><font color="Green">E94</font></i></a>, <a class="ref" href="polynom1.html#T32" target="_self">Th32</a></i>;<br/><b>set </b><font color="Maroon">c<sub>13</sub></font> =  <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span>;<br/><a NAME="E11:158_1"/><i><font color="Green">E98</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <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"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom1.html#E4:158"><i><font color="Green">E93</font></i></a>, <a class="txt" href="polynom1.html#E7:158_1"><i><font color="Green">E95</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>15</sub></font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E13:158_1"/><i><font color="Green">E99</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E14:158_1"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>14</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E2:158"><i><font color="Green">E91</font></i></a>, <a class="txt" href="polynom1.html#E7:158_1"><i><font color="Green">E95</font></i></a>, <a class="ref" href="polynom1.html#T72" target="_self">Th72</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>15</sub></font> as    <a href="polynom1.html#M1" target="_self">Element</a> of  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="polynom1.html#D14" target="_self">Def14</a></i>;<br/><a NAME="E16:158_1"/><i><font color="Green">E101</font></i>: 
( <font color="Maroon">c<sub>16</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>15</sub></font> )
 ;<br/><a NAME="E17:158_1"/><b>then </b><i><font color="Green">E102</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E13:158_1"><i><font color="Green">E99</font></i></a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/><a NAME="E18:158_1"/><i><font color="Green">E103</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E13:158_1"><i><font color="Green">E99</font></i></a>, <a class="txt" href="polynom1.html#E16:158_1"><i><font color="Green">E101</font></i></a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/><i><font color="Green">E104</font></i>:  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></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> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E11:158_1"><i><font color="Green">E98</font></i></a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></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> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>

;<br/><b>then consider </b><font color="Maroon">c<sub>18</sub></font>, <font color="Maroon">c<sub>19</sub></font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E21:158_1"/><i><font color="Green">E105</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E22:158_1"/><i><font color="Green">E106</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E8:158_1"><i><font color="Green">E96</font></i></a>, <a class="txt" href="polynom1.html#E18:158_1"><i><font color="Green">E103</font></i></a>, <a class="ref" href="polynom1.html#T72" target="_self">Th72</a></i>;<br/><a NAME="E23:158_1"/><i><font color="Green">E107</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E8:158_1"><i><font color="Green">E96</font></i></a>, <a class="txt" href="polynom1.html#E19:158_1"><i><font color="Green">E104</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/><a NAME="E24:158_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E25:158_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="polynom1.html#E8:158_1"><i><font color="Green">E96</font></i></a>, <a class="txt" href="polynom1.html#E19:158_1"><i><font color="Green">E104</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/><b>then </b><i><font color="Green">E108</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> = 
<span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>14</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="txt" href="polynom1.html#E8:158_1"><i><font color="Green">E96</font></i></a>, <a class="txt" href="polynom1.html#E11:158_1"><i><font color="Green">E98</font></i></a>, <a class="txt" href="polynom1.html#E17:158_1"><i><font color="Green">E102</font></i></a>, <a class="txt" href="polynom1.html#E21:158_1"><i><font color="Green">E105</font></i></a>, <a class="txt" href="polynom1.html#E23:158_1"><i><font color="Green">E107</font></i></a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="finseq_1.html#K11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
;<br/><a NAME="E27:158_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R6">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E14:158_1"><i><font color="Green">E100</font></i></a>, <a class="txt" href="polynom1.html#E22:158_1"><i><font color="Green">E106</font></i></a>, <a class="ref" href="polynom1.html#T39" target="_self">Th39</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>20</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E29:158_1"/><i><font color="Green">E109</font></i>: 
<font color="Maroon">c<sub>20</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="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E30:158_1"/><i><font color="Green">E110</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>,<font color="Maroon">c<sub>19</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="polynom1.html#T73" target="_self">Th73</a></i>;<br/><b>set </b><font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>14</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>18</sub></font>;<br/><b>consider </b><font color="Maroon">c<sub>22</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E32:158_1"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">c<sub>22</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="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E33:158_1"/><i><font color="Green">E112</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>18</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="polynom1.html#T73" target="_self">Th73</a></i>;<br/><b>set </b><font color="Maroon">c<sub>23</sub></font> =  <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>;<br/><a NAME="E34:158_1"/><i><font color="Green">E113</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom1.html#E1:158"><i><font color="Green">E90</font></i></a>, <a class="txt" href="polynom1.html#E3:158"><i><font color="Green">E92</font></i></a>, <a class="txt" href="polynom1.html#E29:158_1"><i><font color="Green">E109</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>24</sub></font> = <font color="Maroon">c<sub>14</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>18</sub></font>, <font color="Maroon">c<sub>25</sub></font> = <font color="Maroon">c<sub>19</sub></font> as    <a href="polynom1.html#M1" target="_self">Element</a> of  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="polynom1.html#D14" target="_self">Def14</a></i>;<br/><a NAME="E36:158_1"/><i><font color="Green">E114</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>25</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="polynom1.html#E30:158_1"><i><font color="Green">E110</font></i></a></i>;<br/><a NAME="E37:158_1"/><b>then </b><i><font color="Green">E115</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/><a NAME="E38:158_1"/><i><font color="Green">E116</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E36:158_1"><i><font color="Green">E114</font></i></a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/><i><font color="Green">E117</font></i>:  <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>20</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></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> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E34:158_1"><i><font color="Green">E113</font></i></a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></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> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></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> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span>

;<br/><a NAME="E40:158_1"/><i><font color="Green">E118</font></i>: 
<font color="Maroon">c<sub>22</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> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom1.html#E32:158_1"><i><font color="Green">E111</font></i></a>, <a class="txt" href="polynom1.html#E38:158_1"><i><font color="Green">E116</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E41:158_1"/><i><font color="Green">E119</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>22</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E32:158_1"><i><font color="Green">E111</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/><i><font color="Green">E120</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>20</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>22</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E32:158_1"><i><font color="Green">E111</font></i></a>, <a class="txt" href="polynom1.html#E34:158_1"><i><font color="Green">E113</font></i></a>, <a class="txt" href="polynom1.html#E38:158_1"><i><font color="Green">E116</font></i></a>, <a class="txt" href="polynom1.html#E39:158_1"><i><font color="Green">E117</font></i></a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>18</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>19</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span>
<b>by </b><i><a class="txt" href="polynom1.html#E33:158_1"><i><font color="Green">E112</font></i></a>, <a class="txt" href="polynom1.html#E37:158_1"><i><font color="Green">E115</font></i></a>, <a class="txt" href="polynom1.html#E38:158_1"><i><font color="Green">E116</font></i></a>, <a class="txt" href="polynom1.html#E40:158_1"><i><font color="Green">E118</font></i></a>, <a class="txt" href="polynom1.html#E41:158_1"><i><font color="Green">E119</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="finseq_1.html#K11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
;<br/><b>set </b><font color="Maroon">c<sub>26</sub></font> = <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>20</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>22</sub></font>;<br/><a NAME="E43:158_1"/><i><font color="Green">E121</font></i>: 
<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>20</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>22</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>
 <b>by </b><i><a class="txt" href="polynom1.html#E1:158"><i><font color="Green">E90</font></i></a>, <a class="txt" href="polynom1.html#E29:158_1"><i><font color="Green">E109</font></i></a>, <a class="txt" href="polynom1.html#E32:158_1"><i><font color="Green">E111</font></i></a>, <a class="txt" href="polynom1.html#E38:158_1"><i><font color="Green">E116</font></i></a>, <a class="txt" href="polynom1.html#E39:158_1"><i><font color="Green">E117</font></i></a>, <a class="ref" href="polynom1.html#T33" target="_self">Th33</a></i>;<br/><a NAME="E44:158_1"/>
<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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="wsierp_1.html#K8">Sum</a> <span class="p3">(<span class="default"><a href="polynom1.html#K5" target="_self">Card</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K17">|</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>20</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>22</sub></font></span>)</span> <a href="hidden.html#R1">=</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>20</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>22</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E1:158"><i><font color="Green">E90</font></i></a>, <a class="txt" href="polynom1.html#E29:158_1"><i><font color="Green">E109</font></i></a>, <a class="txt" href="polynom1.html#E32:158_1"><i><font color="Green">E111</font></i></a>, <a class="txt" href="polynom1.html#E38:158_1"><i><font color="Green">E116</font></i></a>, <a class="txt" href="polynom1.html#E39:158_1"><i><font color="Green">E117</font></i></a>, <a class="ref" href="polynom1.html#T33" target="_self">Th33</a></i>;<br/><b>hence </b><a NAME="E45:158_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom1.html#E4:158_1"><i><font color="Green">E94</font></i></a>, <a class="txt" href="polynom1.html#E10:158_1"><i><font color="Green">E97</font></i></a>, <a class="txt" href="polynom1.html#E26:158_1"><i><font color="Green">E108</font></i></a>, <a class="txt" href="polynom1.html#E42:158_1"><i><font color="Green">E120</font></i></a>, <a class="txt" href="polynom1.html#E43:158_1"><i><font color="Green">E121</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/></div><b>end;</b></div>
<a NAME="E6:158"/><b>then </b><i><font color="Green">E94</font></i>: 
 <a href="relat_1.html#K2">rng</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="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>
<a NAME="E7:158"/><i><font color="Green">E95</font></i>: 
 <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>3</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="158_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:158_2"/><i><font color="Green">E96</font></i>: 
<font color="Maroon">c<sub>8</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>
 <b>and </b><br/><a NAME="E2:158_2"/><i><font color="Green">E97</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>
 <b>and </b><br/><a NAME="E3:158_2"/><i><font color="Green">E98</font></i>: 
<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>8</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>
 ;<br/>

<b>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="E5:158_2"/><i><font color="Green">E99</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="E6:158_2"/><i><font color="Green">E100</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="E7:158_2"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>8</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="E8:158_2"/><i><font color="Green">E102</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>8</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E1:158_2"><i><font color="Green">E96</font></i></a>, <a class="ref" href="polynom1.html#T32" target="_self">Th32</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E10:158_2"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>12</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="E11:158_2"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>13</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>12</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E12:158_2"/><i><font color="Green">E105</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>12</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>13</sub></font>
 <b>and </b><br/><a NAME="E13:158_2"/><i><font color="Green">E106</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>12</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>13</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="txt" href="polynom1.html#E2:158_2"><i><font color="Green">E97</font></i></a>, <a class="ref" href="polynom1.html#T32" target="_self">Th32</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>14</sub></font> =  <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>;<br/>
<a NAME="E14:158_2"/><i><font color="Green">E107</font></i>: 
<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#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="txt" href="polynom1.html#E3:158"><i><font color="Green">E92</font></i></a>, <a class="txt" href="polynom1.html#E5:158_2"><i><font color="Green">E99</font></i></a></i>;<br/>
<a NAME="E15:158_2"/><i><font color="Green">E108</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E1:158"><i><font color="Green">E90</font></i></a>, <a class="txt" href="polynom1.html#E5:158_2"><i><font color="Green">E99</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>15</sub></font>, <font color="Maroon">c<sub>16</sub></font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E17:158_2"/><i><font color="Green">E109</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E18:158_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>15</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E1:158"><i><font color="Green">E90</font></i></a>, <a class="txt" href="polynom1.html#E5:158_2"><i><font color="Green">E99</font></i></a>, <a class="ref" href="polynom1.html#T72" target="_self">Th72</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>15</sub></font>, <font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>16</sub></font> as    <a href="polynom1.html#M1" target="_self">Element</a> of  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="polynom1.html#D14" target="_self">Def14</a></i>;<br/>
<a NAME="E20:158_2"/><i><font color="Green">E110</font></i>: 
( <font color="Maroon">c<sub>17</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>16</sub></font> )
 
;<br/>
<a NAME="E21:158_2"/><b>then </b><i><font color="Green">E111</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E17:158_2"><i><font color="Green">E109</font></i></a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/>
<a NAME="E22:158_2"/><i><font color="Green">E112</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E17:158_2"><i><font color="Green">E109</font></i></a>, <a class="txt" href="polynom1.html#E20:158_2"><i><font color="Green">E110</font></i></a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/>
<i><font color="Green">E113</font></i>:  <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> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></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> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E14:158_2"><i><font color="Green">E107</font></i></a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></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> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span>

;<br/>
<b>then consider </b><font color="Maroon">c<sub>19</sub></font>, <font color="Maroon">c<sub>20</sub></font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E25:158_2"/><i><font color="Green">E114</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>20</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E26:158_2"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>19</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E6:158_2"><i><font color="Green">E100</font></i></a>, <a class="txt" href="polynom1.html#E21:158_2"><i><font color="Green">E111</font></i></a>, <a class="ref" href="polynom1.html#T72" target="_self">Th72</a></i>;<br/>
<a NAME="E27:158_2"/><i><font color="Green">E116</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</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#E6:158_2"><i><font color="Green">E100</font></i></a>, <a class="txt" href="polynom1.html#E23:158_2"><i><font color="Green">E113</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<a NAME="E28:158_2"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E29:158_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></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"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="polynom1.html#E6:158_2"><i><font color="Green">E100</font></i></a>, <a class="txt" href="polynom1.html#E23:158_2"><i><font color="Green">E113</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<b>then </b><i><font color="Green">E117</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> = 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>20</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>16</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span>
<b>by </b><i><a class="txt" href="polynom1.html#E6:158_2"><i><font color="Green">E100</font></i></a>, <a class="txt" href="polynom1.html#E14:158_2"><i><font color="Green">E107</font></i></a>, <a class="txt" href="polynom1.html#E22:158_2"><i><font color="Green">E112</font></i></a>, <a class="txt" href="polynom1.html#E25:158_2"><i><font color="Green">E114</font></i></a>, <a class="txt" href="polynom1.html#E27:158_2"><i><font color="Green">E116</font></i></a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_1.html#K11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
;<br/>
<b>set </b><font color="Maroon">c<sub>21</sub></font> =  <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>;<br/>
<a NAME="E31:158_2"/><i><font color="Green">E118</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="txt" href="polynom1.html#E3:158"><i><font color="Green">E92</font></i></a>, <a class="txt" href="polynom1.html#E10:158_2"><i><font color="Green">E103</font></i></a></i>;<br/>
<a NAME="E32:158_2"/><i><font color="Green">E119</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E1:158"><i><font color="Green">E90</font></i></a>, <a class="txt" href="polynom1.html#E10:158_2"><i><font color="Green">E103</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>22</sub></font>, <font color="Maroon">c<sub>23</sub></font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E34:158_2"/><i><font color="Green">E120</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>23</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E35:158_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>22</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E1:158"><i><font color="Green">E90</font></i></a>, <a class="txt" href="polynom1.html#E10:158_2"><i><font color="Green">E103</font></i></a>, <a class="ref" href="polynom1.html#T72" target="_self">Th72</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>24</sub></font> = <font color="Maroon">c<sub>22</sub></font>, <font color="Maroon">c<sub>25</sub></font> = <font color="Maroon">c<sub>23</sub></font> as    <a href="polynom1.html#M1" target="_self">Element</a> of  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="polynom1.html#D14" target="_self">Def14</a></i>;<br/>
<a NAME="E37:158_2"/><i><font color="Green">E121</font></i>: 
( <font color="Maroon">c<sub>24</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>22</sub></font> &amp; <font color="Maroon">c<sub>25</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>23</sub></font> )
 
;<br/>
<a NAME="E38:158_2"/><b>then </b><i><font color="Green">E122</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E34:158_2"><i><font color="Green">E120</font></i></a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/>
<a NAME="E39:158_2"/><i><font color="Green">E123</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E34:158_2"><i><font color="Green">E120</font></i></a>, <a class="txt" href="polynom1.html#E37:158_2"><i><font color="Green">E121</font></i></a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/>
<i><font color="Green">E124</font></i>:  <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>12</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></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> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E31:158_2"><i><font color="Green">E118</font></i></a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></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> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span>

;<br/>
<b>then consider </b><font color="Maroon">c<sub>26</sub></font>, <font color="Maroon">c<sub>27</sub></font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E42:158_2"/><i><font color="Green">E125</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>27</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E43:158_2"/><i><font color="Green">E126</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>26</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>27</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E11:158_2"><i><font color="Green">E104</font></i></a>, <a class="txt" href="polynom1.html#E38:158_2"><i><font color="Green">E122</font></i></a>, <a class="ref" href="polynom1.html#T72" target="_self">Th72</a></i>;<br/>
<a NAME="E44:158_2"/><i><font color="Green">E127</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E45:158_2"/><i><font color="Green">E128</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E11:158_2"><i><font color="Green">E104</font></i></a>, <a class="txt" href="polynom1.html#E40:158_2"><i><font color="Green">E124</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<a NAME="E46:158_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="polynom1.html#E11:158_2"><i><font color="Green">E104</font></i></a>, <a class="txt" href="polynom1.html#E40:158_2"><i><font color="Green">E124</font></i></a>, <a class="txt" href="polynom1.html#E44:158_2"><i><font color="Green">E127</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<b>then </b><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>12</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>13</sub></font> = 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>27</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>23</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span>
<b>by </b><i><a class="txt" href="polynom1.html#E11:158_2"><i><font color="Green">E104</font></i></a>, <a class="txt" href="polynom1.html#E31:158_2"><i><font color="Green">E118</font></i></a>, <a class="txt" href="polynom1.html#E39:158_2"><i><font color="Green">E123</font></i></a>, <a class="txt" href="polynom1.html#E42:158_2"><i><font color="Green">E125</font></i></a>, <a class="txt" href="polynom1.html#E45:158_2"><i><font color="Green">E128</font></i></a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>23</sub></font></span><a href="finseq_1.html#K11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
;<br/>
<a NAME="E48:158_2"/><b>then </b><i><font color="Green">E129</font></i>: 
( <font color="Maroon">c<sub>19</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>26</sub></font> &amp; <font color="Maroon">c<sub>20</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>27</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>23</sub></font> )
 
<b>by </b><i><a class="txt" href="polynom1.html#E3:158_2"><i><font color="Green">E98</font></i></a>, <a class="txt" href="polynom1.html#E8:158_2"><i><font color="Green">E102</font></i></a>, <a class="txt" href="polynom1.html#E13:158_2"><i><font color="Green">E106</font></i></a>, <a class="txt" href="polynom1.html#E30:158_2"><i><font color="Green">E117</font></i></a>, <a class="ref" href="group_7.html#T3">GROUP_7:3</a></i>;<br/>
<a NAME="E49:158_2"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E1:158"><i><font color="Green">E90</font></i></a>, <a class="txt" href="polynom1.html#E5:158_2"><i><font color="Green">E99</font></i></a>, <a class="txt" href="polynom1.html#E10:158_2"><i><font color="Green">E103</font></i></a>, <a class="txt" href="polynom1.html#E15:158_2"><i><font color="Green">E108</font></i></a>, <a class="txt" href="polynom1.html#E17:158_2"><i><font color="Green">E109</font></i></a>, <a class="txt" href="polynom1.html#E26:158_2"><i><font color="Green">E115</font></i></a>, <a class="txt" href="polynom1.html#E32:158_2"><i><font color="Green">E119</font></i></a>, <a class="txt" href="polynom1.html#E34:158_2"><i><font color="Green">E120</font></i></a>, <a class="txt" href="polynom1.html#E43:158_2"><i><font color="Green">E126</font></i></a>, <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E50:158_2"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E6:158_2"><i><font color="Green">E100</font></i></a>, <a class="txt" href="polynom1.html#E7:158_2"><i><font color="Green">E101</font></i></a>, <a class="txt" href="polynom1.html#E11:158_2"><i><font color="Green">E104</font></i></a>, <a class="txt" href="polynom1.html#E12:158_2"><i><font color="Green">E105</font></i></a>, <a class="txt" href="polynom1.html#E25:158_2"><i><font color="Green">E114</font></i></a>, <a class="txt" href="polynom1.html#E27:158_2"><i><font color="Green">E116</font></i></a>, <a class="txt" href="polynom1.html#E40:158_2"><i><font color="Green">E124</font></i></a>, <a class="txt" href="polynom1.html#E42:158_2"><i><font color="Green">E125</font></i></a>, <a class="txt" href="polynom1.html#E45:158_2"><i><font color="Green">E128</font></i></a>, <a class="txt" href="polynom1.html#E48:158_2"><i><font color="Green">E129</font></i></a>, <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E8:158"/>
 <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>4</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="158_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:158_3"/><i><font color="Green">E96</font></i>: 
<font color="Maroon">c<sub>8</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>4</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E2:158_3"/><i><font color="Green">E97</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>4</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E3:158_3"/><i><font color="Green">E98</font></i>: 
<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</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>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/>

<b>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="E5:158_3"/><i><font color="Green">E99</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>4</sub></font>
 <b>and </b><br/><a NAME="E6:158_3"/><i><font color="Green">E100</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>4</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="E7:158_3"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>8</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>4</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="E8:158_3"/><i><font color="Green">E102</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E1:158_3"><i><font color="Green">E96</font></i></a>, <a class="ref" href="polynom1.html#T32" target="_self">Th32</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E10:158_3"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E11:158_3"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>13</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>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E12:158_3"/><i><font color="Green">E105</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>4</sub></font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>12</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>13</sub></font>
 <b>and </b><br/><a NAME="E13:158_3"/><i><font color="Green">E106</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>13</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>4</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#E2:158_3"><i><font color="Green">E97</font></i></a>, <a class="ref" href="polynom1.html#T32" target="_self">Th32</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>14</sub></font> =  <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span>;<br/>
<a NAME="E14:158_3"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</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#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="polynom1.html#E4:158"><i><font color="Green">E93</font></i></a>, <a class="txt" href="polynom1.html#E5:158_3"><i><font color="Green">E99</font></i></a></i>;<br/>
<a NAME="E15:158_3"/><i><font color="Green">E108</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E2:158"><i><font color="Green">E91</font></i></a>, <a class="txt" href="polynom1.html#E5:158_3"><i><font color="Green">E99</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>15</sub></font>, <font color="Maroon">c<sub>16</sub></font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E17:158_3"/><i><font color="Green">E109</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E18:158_3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>15</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E2:158"><i><font color="Green">E91</font></i></a>, <a class="txt" href="polynom1.html#E5:158_3"><i><font color="Green">E99</font></i></a>, <a class="ref" href="polynom1.html#T72" target="_self">Th72</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>15</sub></font>, <font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>16</sub></font> as    <a href="polynom1.html#M1" target="_self">Element</a> of  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="polynom1.html#D14" target="_self">Def14</a></i>;<br/>
<a NAME="E20:158_3"/><i><font color="Green">E110</font></i>: 
( <font color="Maroon">c<sub>17</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>16</sub></font> )
 
;<br/>
<a NAME="E21:158_3"/><b>then </b><i><font color="Green">E111</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E17:158_3"><i><font color="Green">E109</font></i></a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/>
<a NAME="E22:158_3"/><i><font color="Green">E112</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E17:158_3"><i><font color="Green">E109</font></i></a>, <a class="txt" href="polynom1.html#E20:158_3"><i><font color="Green">E110</font></i></a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/>
<i><font color="Green">E113</font></i>:  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></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> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E14:158_3"><i><font color="Green">E107</font></i></a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></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> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>

;<br/>
<b>then consider </b><font color="Maroon">c<sub>19</sub></font>, <font color="Maroon">c<sub>20</sub></font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E25:158_3"/><i><font color="Green">E114</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>20</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E26:158_3"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>19</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E6:158_3"><i><font color="Green">E100</font></i></a>, <a class="txt" href="polynom1.html#E22:158_3"><i><font color="Green">E112</font></i></a>, <a class="ref" href="polynom1.html#T72" target="_self">Th72</a></i>;<br/>
<a NAME="E27:158_3"/><i><font color="Green">E116</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E28:158_3"/><i><font color="Green">E117</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</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#E6:158_3"><i><font color="Green">E100</font></i></a>, <a class="txt" href="polynom1.html#E23:158_3"><i><font color="Green">E113</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<a NAME="E29:158_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></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"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="polynom1.html#E6:158_3"><i><font color="Green">E100</font></i></a>, <a class="txt" href="polynom1.html#E23:158_3"><i><font color="Green">E113</font></i></a>, <a class="txt" href="polynom1.html#E27:158_3"><i><font color="Green">E116</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<b>then </b><i><font color="Green">E118</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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 class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>15</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>20</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="txt" href="polynom1.html#E6:158_3"><i><font color="Green">E100</font></i></a>, <a class="txt" href="polynom1.html#E14:158_3"><i><font color="Green">E107</font></i></a>, <a class="txt" href="polynom1.html#E21:158_3"><i><font color="Green">E111</font></i></a>, <a class="txt" href="polynom1.html#E25:158_3"><i><font color="Green">E114</font></i></a>, <a class="txt" href="polynom1.html#E28:158_3"><i><font color="Green">E117</font></i></a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>20</sub></font></span><a href="finseq_1.html#K11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
;<br/>
<b>set </b><font color="Maroon">c<sub>21</sub></font> =  <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span>;<br/>
<a NAME="E31:158_3"/><i><font color="Green">E119</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</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#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="polynom1.html#E4:158"><i><font color="Green">E93</font></i></a>, <a class="txt" href="polynom1.html#E10:158_3"><i><font color="Green">E103</font></i></a></i>;<br/>
<a NAME="E32:158_3"/><i><font color="Green">E120</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E2:158"><i><font color="Green">E91</font></i></a>, <a class="txt" href="polynom1.html#E10:158_3"><i><font color="Green">E103</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>22</sub></font>, <font color="Maroon">c<sub>23</sub></font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E34:158_3"/><i><font color="Green">E121</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>23</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E35:158_3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>22</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E2:158"><i><font color="Green">E91</font></i></a>, <a class="txt" href="polynom1.html#E10:158_3"><i><font color="Green">E103</font></i></a>, <a class="ref" href="polynom1.html#T72" target="_self">Th72</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>24</sub></font> = <font color="Maroon">c<sub>22</sub></font>, <font color="Maroon">c<sub>25</sub></font> = <font color="Maroon">c<sub>23</sub></font> as    <a href="polynom1.html#M1" target="_self">Element</a> of  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="polynom1.html#D14" target="_self">Def14</a></i>;<br/>
<a NAME="E37:158_3"/><i><font color="Green">E122</font></i>: 
( <font color="Maroon">c<sub>24</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>22</sub></font> &amp; <font color="Maroon">c<sub>25</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>23</sub></font> )
 
;<br/>
<a NAME="E38:158_3"/><b>then </b><i><font color="Green">E123</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E34:158_3"><i><font color="Green">E121</font></i></a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/>
<a NAME="E39:158_3"/><i><font color="Green">E124</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E34:158_3"><i><font color="Green">E121</font></i></a>, <a class="txt" href="polynom1.html#E37:158_3"><i><font color="Green">E122</font></i></a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/>
<i><font color="Green">E125</font></i>:  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></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> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E31:158_3"><i><font color="Green">E119</font></i></a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></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> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>

;<br/>
<b>then consider </b><font color="Maroon">c<sub>26</sub></font>, <font color="Maroon">c<sub>27</sub></font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E42:158_3"/><i><font color="Green">E126</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>27</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E43:158_3"/><i><font color="Green">E127</font></i>: 
<font color="Maroon">c<sub>23</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>26</sub></font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>27</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E11:158_3"><i><font color="Green">E104</font></i></a>, <a class="txt" href="polynom1.html#E39:158_3"><i><font color="Green">E124</font></i></a>, <a class="ref" href="polynom1.html#T72" target="_self">Th72</a></i>;<br/>
<a NAME="E44:158_3"/><i><font color="Green">E128</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E11:158_3"><i><font color="Green">E104</font></i></a>, <a class="txt" href="polynom1.html#E40:158_3"><i><font color="Green">E125</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<a NAME="E45:158_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E46:158_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&gt;</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="polynom1.html#E11:158_3"><i><font color="Green">E104</font></i></a>, <a class="txt" href="polynom1.html#E40:158_3"><i><font color="Green">E125</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>13</sub></font> = 
<span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>22</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>27</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="txt" href="polynom1.html#E11:158_3"><i><font color="Green">E104</font></i></a>, <a class="txt" href="polynom1.html#E31:158_3"><i><font color="Green">E119</font></i></a>, <a class="txt" href="polynom1.html#E38:158_3"><i><font color="Green">E123</font></i></a>, <a class="txt" href="polynom1.html#E42:158_3"><i><font color="Green">E126</font></i></a>, <a class="txt" href="polynom1.html#E44:158_3"><i><font color="Green">E128</font></i></a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>27</sub></font></span><a href="finseq_1.html#K11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
;<br/>
<a NAME="E48:158_3"/><b>then </b><i><font color="Green">E129</font></i>: 
( <font color="Maroon">c<sub>19</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>26</sub></font> &amp; <font color="Maroon">c<sub>20</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>27</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>22</sub></font> )
 
<b>by </b><i><a class="txt" href="polynom1.html#E3:158_3"><i><font color="Green">E98</font></i></a>, <a class="txt" href="polynom1.html#E8:158_3"><i><font color="Green">E102</font></i></a>, <a class="txt" href="polynom1.html#E13:158_3"><i><font color="Green">E106</font></i></a>, <a class="txt" href="polynom1.html#E30:158_3"><i><font color="Green">E118</font></i></a>, <a class="ref" href="group_7.html#T3">GROUP_7:3</a></i>;<br/>
<a NAME="E49:158_3"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E2:158"><i><font color="Green">E91</font></i></a>, <a class="txt" href="polynom1.html#E5:158_3"><i><font color="Green">E99</font></i></a>, <a class="txt" href="polynom1.html#E10:158_3"><i><font color="Green">E103</font></i></a>, <a class="txt" href="polynom1.html#E15:158_3"><i><font color="Green">E108</font></i></a>, <a class="txt" href="polynom1.html#E17:158_3"><i><font color="Green">E109</font></i></a>, <a class="txt" href="polynom1.html#E26:158_3"><i><font color="Green">E115</font></i></a>, <a class="txt" href="polynom1.html#E32:158_3"><i><font color="Green">E120</font></i></a>, <a class="txt" href="polynom1.html#E34:158_3"><i><font color="Green">E121</font></i></a>, <a class="txt" href="polynom1.html#E43:158_3"><i><font color="Green">E127</font></i></a>, <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E50:158_3"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E6:158_3"><i><font color="Green">E100</font></i></a>, <a class="txt" href="polynom1.html#E7:158_3"><i><font color="Green">E101</font></i></a>, <a class="txt" href="polynom1.html#E11:158_3"><i><font color="Green">E104</font></i></a>, <a class="txt" href="polynom1.html#E12:158_3"><i><font color="Green">E105</font></i></a>, <a class="txt" href="polynom1.html#E25:158_3"><i><font color="Green">E114</font></i></a>, <a class="txt" href="polynom1.html#E28:158_3"><i><font color="Green">E117</font></i></a>, <a class="txt" href="polynom1.html#E40:158_3"><i><font color="Green">E125</font></i></a>, <a class="txt" href="polynom1.html#E42:158_3"><i><font color="Green">E126</font></i></a>, <a class="txt" href="polynom1.html#E44:158_3"><i><font color="Green">E128</font></i></a>, <a class="txt" href="polynom1.html#E48:158_3"><i><font color="Green">E129</font></i></a>, <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:158"/><b>then </b>
 <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>3</sub></font>, <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>4</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 
<b>by </b><i><a class="txt" href="polynom1.html#E6:158"><i><font color="Green">E94</font></i></a>, <a class="txt" href="polynom1.html#E7:158"><i><font color="Green">E95</font></i></a>, <a class="ref" href="rfinseq.html#T39">RFINSEQ:39</a></i>;<br/>
<b>hence </b><a NAME="E10:158"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="funct_2.html#NM2">Permutation</a> of  <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> st  <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>4</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="partfun1.html#K1">*</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="rfinseq.html#T17">RFINSEQ:17</a></i>;<br/>


</div>
