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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  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V3">Abelian</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> <a href="group_1.html#V4">associative</a> <a href="vectsp_1.html#V7">distributive</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="polynom1.html#NM3">Series</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>





<b>set </b><font color="Maroon">c<sub>6</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="173_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>7</sub></font> be    <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>;<br/><b>consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E2:173_1"/><i><font color="Green">E100</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K28" target="_self">*'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K23" target="_self">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">c<sub>8</sub></font>
 <b>and </b><br/><a NAME="E3:173_1"/><i><font color="Green">E101</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E4:173_1"/><i><font color="Green">E102</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>8</sub></font> holds <br/>ex <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K23" target="_self">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="polynom1.html#K15" target="_self">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="polynom1.html#D26" target="_self">Def26</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>9</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E6:173_1"/><i><font color="Green">E103</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K28" target="_self">*'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">c<sub>9</sub></font>
 <b>and </b><br/><a NAME="E7:173_1"/><i><font color="Green">E104</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E8:173_1"/><i><font color="Green">E105</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>9</sub></font> holds <br/>ex <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="polynom1.html#D26" target="_self">Def26</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>10</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E10:173_1"/><i><font color="Green">E106</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K28" target="_self">*'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">c<sub>10</sub></font>
 <b>and </b><br/><a NAME="E11:173_1"/><i><font color="Green">E107</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E12:173_1"/><i><font color="Green">E108</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>10</sub></font> holds <br/>ex <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="polynom1.html#D26" target="_self">Def26</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>10</sub></font> as    <a href="finseq_2.html#M2">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="polynom1.html#E3:173_1"><i><font color="Green">E101</font></i></a>, <a class="txt" href="polynom1.html#E7:173_1"><i><font color="Green">E104</font></i></a>, <a class="txt" href="polynom1.html#E11:173_1"><i><font color="Green">E107</font></i></a>, <a class="ref" href="finseq_2.html#T110">FINSEQ_2:110</a></i>;<br/><a NAME="E14:173_1"/><i><font color="Green">E109</font></i>: 
(  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>8</sub></font> &amp;  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="txt" href="polynom1.html#E3:173_1"><i><font color="Green">E101</font></i></a>, <a class="txt" href="polynom1.html#E7:173_1"><i><font color="Green">E104</font></i></a>, <a class="txt" href="polynom1.html#E11:173_1"><i><font color="Green">E107</font></i></a>, <a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><a NAME="E15:173_1"/><b>then </b><i><font color="Green">E110</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="fvsum_1.html#K4">+</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="polynom1.html#T5" target="_self">Th5</a></i>;<br/><a NAME="E16:173_1"/><b>then </b><i><font color="Green">E111</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="fvsum_1.html#K4">+</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="173_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>14</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:173_1_1"/>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
 ;<br/><a NAME="E2:173_1_1"/><b>then </b>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E3:173_1_1"/><b>then </b><i><font color="Green">E112</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>then 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="E5:173_1_1"/><i><font color="Green">E113</font></i>: 
( <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>14</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> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K23" target="_self">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="polynom1.html#E4:173_1"><i><font color="Green">E102</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>17</sub></font>, <font color="Maroon">c<sub>18</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="E7:173_1_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>7</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>14</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>17</sub></font>,<font color="Maroon">c<sub>18</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="polynom1.html#E8:173_1"><i><font color="Green">E105</font></i></a>, <a class="txt" href="polynom1.html#E14:173_1"><i><font color="Green">E109</font></i></a>, <a class="txt" href="polynom1.html#E3:173_1_1"><i><font color="Green">E112</font></i></a></i>;<br/><b>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="E9:173_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>7</sub></font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">c<sub>14</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> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="polynom1.html#E12:173_1"><i><font color="Green">E108</font></i></a>, <a class="txt" href="polynom1.html#E14:173_1"><i><font color="Green">E109</font></i></a>, <a class="txt" href="polynom1.html#E3:173_1_1"><i><font color="Green">E112</font></i></a></i>;<br/><a NAME="E10:173_1_1"/><i><font color="Green">E116</font></i>: 
( <font color="Maroon">c<sub>15</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>19</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>20</sub></font> )
 <b>by </b><i><a class="txt" href="polynom1.html#E5:173_1_1"><i><font color="Green">E113</font></i></a>, <a class="txt" href="polynom1.html#E7:173_1_1"><i><font color="Green">E114</font></i></a>, <a class="txt" href="polynom1.html#E9:173_1_1"><i><font color="Green">E115</font></i></a>, <a class="ref" href="group_7.html#T2">GROUP_7:2</a></i>;<br/><a NAME="E11:173_1_1"/><i><font color="Green">E117</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> )
 <b>by </b><i><a class="txt" href="polynom1.html#E14:173_1"><i><font color="Green">E109</font></i></a>, <a class="txt" href="polynom1.html#E3:173_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/><b>hence </b><font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E5:173_1_1"><i><font color="Green">E113</font></i></a>, <a class="ref" href="polynom1.html#D21" target="_self">Def21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D18">VECTSP_1:def 18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="fvsum_1.html#K4">+</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
<b>by </b><i><a class="txt" href="polynom1.html#E15:173_1"><i><font color="Green">E110</font></i></a>, <a class="txt" href="polynom1.html#E3:173_1_1"><i><font color="Green">E112</font></i></a>, <a class="txt" href="polynom1.html#E7:173_1_1"><i><font color="Green">E114</font></i></a>, <a class="txt" href="polynom1.html#E9:173_1_1"><i><font color="Green">E115</font></i></a>, <a class="txt" href="polynom1.html#E10:173_1_1"><i><font color="Green">E116</font></i></a>, <a class="txt" href="polynom1.html#E11:173_1_1"><i><font color="Green">E117</font></i></a>, <a class="ref" href="fvsum_1.html#T21">FVSUM_1:21</a></i>
;<br/><br/></div><b>end;</b></div><a NAME="E18:173_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> <a href="fvsum_1.html#K4">+</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="polynom1.html#E16:173_1"><i><font color="Green">E111</font></i></a>, <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K28" target="_self">*'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K23" target="_self">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">c<sub>13</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E2:173_1"><i><font color="Green">E100</font></i></a>, <a class="ref" href="fvsum_1.html#T95">FVSUM_1:95</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K28" target="_self">*'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K23" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K28" target="_self">*'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="polynom1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="polynom1.html#E6:173_1"><i><font color="Green">E103</font></i></a>, <a class="txt" href="polynom1.html#E10:173_1"><i><font color="Green">E106</font></i></a>, <a class="ref" href="polynom1.html#D21" target="_self">Def21</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:173"/>
<font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K28" target="_self">*'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K23" target="_self">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K28" target="_self">*'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K23" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K28" target="_self">*'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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