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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>, <font color="Maroon">c<sub>3</sub></font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:23"/><i><font color="Green">E16</font></i>: 
 <a href="relat_1.html#K3">field</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="wellord2.html#D1">WELLORD2:def 1</a></i>;<br/>
<a NAME="E2:23"/>
 <a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font> is <a href="wellord1.html#V2">well-ordering</a>
 
<b>by </b><i><a class="ref" href="wellord2.html#T7">WELLORD2:7</a></i>;<br/>
<a NAME="E3:23"/><b>then </b>
 <a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font> is <a href="orders_1.html#V3">being_linear-order</a>
 
<b>by </b><i><a class="ref" href="orders_1.html#T107">ORDERS_1:107</a></i>;<br/>
<a NAME="E4:23"/><b>then </b><i><font color="Green">E17</font></i>: 
 <a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font> <a href="orders_1.html#R3">linearly_orders</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="bagorder.html#E1:23"><i><font color="Green">E16</font></i></a>, <a class="ref" href="orders_1.html#T133">ORDERS_1:133</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E6:23"/><i><font color="Green">E18</font></i>: 
 <a href="bagorder.html#K3" target="_self">TotDegree</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="wsierp_1.html#K8">Sum</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E7:23"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="polynom2.html#K2">*</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1">support</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="bagorder.html#D4" target="_self">Def4</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E9:23"/><i><font color="Green">E20</font></i>: 
 <a href="bagorder.html#K3" target="_self">TotDegree</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="wsierp_1.html#K8">Sum</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E10:23"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="polynom2.html#K2">*</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1">support</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="bagorder.html#D4" target="_self">Def4</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E12:23"/><i><font color="Green">E22</font></i>: 
 <a href="bagorder.html#K3" target="_self">TotDegree</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="wsierp_1.html#K8">Sum</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E13:23"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="polynom2.html#K2">*</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1">support</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="bagorder.html#D4" target="_self">Def4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</sub></font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T27">FINSEQ_2:27</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1">(<span class="default"><a href="polynom2.html#K1">support</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finsub_1.html#K1">\/</a> <span class="p1">(<span class="default"><a href="polynom2.html#K1">support</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <span class="p1">(<span class="default"><a href="polynom2.html#K1">support</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finsub_1.html#K1">\/</a> <span class="p1">(<span class="default"><a href="polynom2.html#K1">support</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> as  <a href="finset_1.html#V1">finite</a> <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> =  <a href="triang_1.html#K2">SgmX</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>9</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="polynom2.html#K2">*</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>9</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="polynom2.html#K2">*</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>9</sub></font></span>)</span>;<br/>
<a NAME="E16:23"/>
 <a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font> <a href="orders_1.html#R3">linearly_orders</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="bagorder.html#E4:23"><i><font color="Green">E17</font></i></a>, <a class="ref" href="orders_1.html#T134">ORDERS_1:134</a></i>;<br/>
<a NAME="E17:23"/><b>then </b><i><font color="Green">E24</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="triang_1.html#D2">TRIANG_1:def 2</a></i>;<br/>
<a NAME="E18:23"/><i><font color="Green">E25</font></i>: 
 <a href="polynom2.html#K1">support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="polynom1.html#T42">POLYNOM1:42</a></i>;<br/>
<a NAME="E19:23"/><i><font color="Green">E26</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="polynom2.html#K2">*</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>9</sub></font></span>)</span>, <font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="polynom2.html#K2">*</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>9</sub></font></span>)</span> as   <a href="finseq_1.html#NM1">FinSequence</a> <b>by </b><i><a class="txt" href="bagorder.html#E17:23"><i><font color="Green">E24</font></i></a>, <a class="ref" href="finseq_1.html#T20">FINSEQ_1:20</a></i>;<br/>
<a NAME="E21:23"/><i><font color="Green">E27</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K5">NAT</a>  &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K5">NAT</a>  )
 
<b>by </b><i><a class="ref" href="seqm_3.html#D8">SEQM_3:def 8</a></i>;<br/>
<a NAME="E22:23"/>
(  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>13</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>14</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T45">RELAT_1:45</a></i>;<br/>
<a NAME="E23:23"/><b>then </b><i><font color="Green">E28</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>13</sub></font> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K5">NAT</a>  &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>14</sub></font> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K5">NAT</a>  )
 
<b>by </b><i><a class="txt" href="bagorder.html#E21:23"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E24:23"/><b>then </b>
(  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>13</sub></font> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K1">REAL</a>  &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>14</sub></font> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K1">REAL</a>  )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>14</sub></font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a>  <b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</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="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="txt" href="bagorder.html#E23:23"><i><font color="Green">E28</font></i></a>, <a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>19</sub></font> =  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<a NAME="E27:23"/><i><font color="Green">E29</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<i><font color="Green">E30</font></i>:  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font>
<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="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="bagorder.html#E7:23"><i><font color="Green">E19</font></i></a>, <a class="txt" href="bagorder.html#E17:23"><i><font color="Green">E24</font></i></a>, <a class="txt" href="bagorder.html#E18:23"><i><font color="Green">E25</font></i></a>, <a class="txt" href="bagorder.html#E27:23"><i><font color="Green">E29</font></i></a>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>
;<br/>
<a NAME="E29:23"/><b>then </b><i><font color="Green">E31</font></i>: 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="txt" href="bagorder.html#E17:23"><i><font color="Green">E24</font></i></a>, <a class="txt" href="bagorder.html#E19:23"><i><font color="Green">E26</font></i></a>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/>
<a NAME="E30:23"/><i><font color="Green">E32</font></i>: 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="bagorder.html#E17:23"><i><font color="Green">E24</font></i></a>, <a class="txt" href="bagorder.html#E19:23"><i><font color="Green">E26</font></i></a>, <a class="txt" href="bagorder.html#E28:23"><i><font color="Green">E30</font></i></a>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/>
<a NAME="E31:23"/><i><font color="Green">E33</font></i>: 
 <a href="wsierp_1.html#K8">Sum</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="wsierp_1.html#K8">Sum</a> <font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="bagorder.html#E10:23"><i><font color="Green">E21</font></i></a>, <a class="ref" href="bagorder.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E32:23"/><i><font color="Green">E34</font></i>: 
 <a href="wsierp_1.html#K8">Sum</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="wsierp_1.html#K8">Sum</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="bagorder.html#E13:23"><i><font color="Green">E23</font></i></a>, <a class="ref" href="bagorder.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E33:23"/><i><font color="Green">E35</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="bagorder.html#E29:23"><i><font color="Green">E31</font></i></a>, <a class="txt" href="bagorder.html#E30:23"><i><font color="Green">E32</font></i></a>, <a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/>
<a NAME="E34:23"/><b>then </b><i><font color="Green">E36</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="rvsum_1.html#K3">+</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="ref" href="integra5.html#T2">INTEGRA5:2</a></i>;<br/>
<a NAME="E35:23"/><b>then </b><i><font color="Green">E37</font></i>: 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="rvsum_1.html#K3">+</a> <font color="Maroon">c<sub>16</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="bagorder.html#E29:23"><i><font color="Green">E31</font></i></a>, <a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>15</sub></font> as  <a href="seqm_3.html#V6">natural-yielding</a>  <a href="pboole.html#M1">ManySortedSet</a> of  <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>4</sub></font></span>)</span> <b>by </b><i><a class="txt" href="bagorder.html#E23:23"><i><font color="Green">E28</font></i></a>, <a class="txt" href="bagorder.html#E29:23"><i><font color="Green">E31</font></i></a>, <a class="ref" href="pboole.html#D3">PBOOLE:def 3</a>, <a class="ref" href="seqm_3.html#D8">SEQM_3:def 8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:23_2"/>
 <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>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>thus </b><a NAME="E2:23_2"/>
 <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>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="rvsum_1.html#K3">+</a> <font color="Maroon">c<sub>16</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="bagorder.html#E29:23"><i><font color="Green">E31</font></i></a>, <a class="txt" href="bagorder.html#E34:23"><i><font color="Green">E36</font></i></a>, <a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><b>let </b><font color="Maroon">c<sub>21</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E3:23_2"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>21</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>4</sub></font></span>)</span>
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>15</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>21</sub></font>, <font color="Maroon">c<sub>23</sub></font> = <font color="Maroon">c<sub>16</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>21</sub></font> as   <a href="real_1.html#NM1">Real</a> ;<br/><b>thus </b><font color="Maroon">c<sub>7</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>21</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="polynom1.html#K8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1">support</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>21</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="bagorder.html#E7:23"><i><font color="Green">E19</font></i></a>, <a class="txt" href="bagorder.html#E18:23"><i><font color="Green">E25</font></i></a>, <a class="txt" href="bagorder.html#E28:23"><i><font color="Green">E30</font></i></a>, <a class="txt" href="bagorder.html#E3:23_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#K8">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p4">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="polynom2.html#K1">support</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>21</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K8">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p4">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="polynom2.html#K1">support</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>21</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D5">POLYNOM1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>21</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K8">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p4">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="polynom2.html#K1">support</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>21</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="bagorder.html#E18:23"><i><font color="Green">E25</font></i></a>, <a class="txt" href="bagorder.html#E28:23"><i><font color="Green">E30</font></i></a>, <a class="txt" href="bagorder.html#E3:23_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">c<sub>22</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>23</sub></font>
<b>by </b><i><a class="txt" href="bagorder.html#E18:23"><i><font color="Green">E25</font></i></a>, <a class="txt" href="bagorder.html#E28:23"><i><font color="Green">E30</font></i></a>, <a class="txt" href="bagorder.html#E3:23_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="rvsum_1.html#K3">+</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>21</sub></font>
<b>by </b><i><a class="txt" href="bagorder.html#E35:23"><i><font color="Green">E37</font></i></a>, <a class="txt" href="bagorder.html#E3:23_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="rvsum_1.html#T26">RVSUM_1:26</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E38:23"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> <a href="rvsum_1.html#K3">+</a> <font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T17">FINSEQ_1:17</a></i>;<br/>
<b>hence </b><a NAME="E39:23"/>
 <a href="bagorder.html#K3" target="_self">TotDegree</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="bagorder.html#K3" target="_self">TotDegree</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="bagorder.html#K3" target="_self">TotDegree</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="bagorder.html#E6:23"><i><font color="Green">E18</font></i></a>, <a class="txt" href="bagorder.html#E9:23"><i><font color="Green">E20</font></i></a>, <a class="txt" href="bagorder.html#E12:23"><i><font color="Green">E22</font></i></a>, <a class="txt" href="bagorder.html#E31:23"><i><font color="Green">E33</font></i></a>, <a class="txt" href="bagorder.html#E32:23"><i><font color="Green">E34</font></i></a>, <a class="txt" href="bagorder.html#E33:23"><i><font color="Green">E35</font></i></a>, <a class="ref" href="integra5.html#T2">INTEGRA5:2</a></i>;<br/>


</div>
