<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="polynom1.html#NM4">Polynomial</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K10">+^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:14_1_2"/><i><font color="Green">E9</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K10">+^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>ex <font color="Olive">b<sub>2</sub></font> being   <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>3</sub></font> being   <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>2</sub></font>ex <font color="Olive">b<sub>4</sub></font> being  <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> st <br/>( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K15">.</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="pboole.html#R6">=</a> <font color="Olive">b<sub>2</sub></font> <a href="polynom6.html#K1" target="_self">+^</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="polynom1.html#K15">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> <a href="polynom1.html#K15">.</a> <font color="Olive">b<sub>3</sub></font> )
 <b>and </b><br/><a NAME="E2:14_1_2"/><i><font color="Green">E10</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K10">+^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>ex <font color="Olive">b<sub>2</sub></font> being   <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>3</sub></font> being   <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>2</sub></font>ex <font color="Olive">b<sub>4</sub></font> being  <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> st <br/>( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K15">.</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="pboole.html#R6">=</a> <font color="Olive">b<sub>2</sub></font> <a href="polynom6.html#K1" target="_self">+^</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="polynom1.html#K15">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> <a href="polynom1.html#K15">.</a> <font color="Olive">b<sub>3</sub></font> )
 ;<br/>

<a NAME="E3:14_1_2"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K10">+^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> holds <font color="Maroon">c<sub>5</sub></font> <a href="polynom1.html#K15">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="polynom1.html#K15">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K10">+^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>

<b>consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>10</sub></font> being   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E2:14_1_2_1"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>8</sub></font>
 <b>and </b><br/><a NAME="E3:14_1_2_1"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="polynom6.html#K1" target="_self">+^</a> <font color="Maroon">c<sub>9</sub></font>
 <b>and </b><br/><a NAME="E4:14_1_2_1"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="polynom6.html#E1:14_1_2"><i><font color="Green">E9</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>11</sub></font> being    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>12</sub></font> being    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>13</sub></font> being   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E6:14_1_2_1"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>11</sub></font>
 <b>and </b><br/><a NAME="E7:14_1_2_1"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="polynom6.html#K1" target="_self">+^</a> <font color="Maroon">c<sub>12</sub></font>
 <b>and </b><br/><a NAME="E8:14_1_2_1"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="polynom6.html#E2:14_1_2"><i><font color="Green">E10</font></i></a></i>;<br/>
<a NAME="E9:14_1_2_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="polynom6.html#E3:14_1_2_1"><i><font color="Green">E12</font></i></a>, <a class="txt" href="polynom6.html#E7:14_1_2_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="polynom6.html#T7" target="_self">Th7</a></i>;<br/>
<b>hence </b><a NAME="E10:14_1_2_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="polynom6.html#E2:14_1_2_1"><i><font color="Green">E11</font></i></a>, <a class="txt" href="polynom6.html#E3:14_1_2_1"><i><font color="Green">E12</font></i></a>, <a class="txt" href="polynom6.html#E4:14_1_2_1"><i><font color="Green">E13</font></i></a>, <a class="txt" href="polynom6.html#E6:14_1_2_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="polynom6.html#E7:14_1_2_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="polynom6.html#E8:14_1_2_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="polynom6.html#T7" target="_self">Th7</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:14_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


</div>
