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<b>let </b><font color="Maroon">B1</font> be   <a href="orders_1.html#NM2">Order</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>, <font color="Maroon">B2</font> be   <a href="orders_1.html#NM2">Order</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:47_1_2"/><i><font color="Green">E77</font></i>: 
for <font color="Olive">p</font>, <font color="Olive">q</font> being  <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font> holds <br/> ( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">p</font>,<font color="Olive">q</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</font> iff <font color="Olive">p</font> <a href="polynom1.html#R3">divides</a> <font color="Olive">q</font> )
 <b>and </b><br/><a NAME="E2:47_1_2"/><i><font color="Green">E78</font></i>: 
for <font color="Olive">p</font>, <font color="Olive">q</font> being  <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font> holds <br/> ( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">p</font>,<font color="Olive">q</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">B2</font> iff <font color="Olive">p</font> <a href="polynom1.html#R3">divides</a> <font color="Olive">q</font> )
 ;<br/>

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="relat_1.html#D2">RELAT_1:def 2</a><br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:47_1_2_1"/><i><font color="Green">E79</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</font>
 ;<br/><b>then consider </b><font color="Maroon">b1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">b2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:47_1_2_1"/><i><font color="Green">E80</font></i>: 
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b2</font></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">b1</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> &amp; <font color="Maroon">b2</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> )
 <b>by </b><i><a class="ref" href="relset_1.html#T6">RELSET_1:6</a></i>;<br/><b>reconsider </b><font color="Maroon">b1</font> = <font color="Maroon">b1</font>, <font color="Maroon">b2</font> = <font color="Maroon">b2</font> as   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font> <b>by </b><i>, <a class="ref" href="polynom1.html#D14">POLYNOM1:def 14</a></i>;<br/><a NAME="E5:47_1_2_1"/>
<font color="Maroon">b1</font> <a href="polynom1.html#R3">divides</a> <font color="Maroon">b2</font>
 <b>by </b><i><a class="ref" href="groeb_1.html#T1" target="_self">Th1</a>, , </i>;<br/><b>hence </b><a NAME="E6:47_1_2_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">B2</font>
 <b>by </b><i>, </i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E4:47_1_2"/><i><font color="Green">E81</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">B2</font>
 ;<br/>

<b>then consider </b><font color="Maroon">b1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">b2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:47_1_2"/><i><font color="Green">E82</font></i>: 
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b2</font></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">b1</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> &amp; <font color="Maroon">b2</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> )
 <b>by </b><i><a class="ref" href="relset_1.html#T6">RELSET_1:6</a></i>;<br/>
<b>reconsider </b><font color="Maroon">b1</font> = <font color="Maroon">b1</font>, <font color="Maroon">b2</font> = <font color="Maroon">b2</font> as   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font> <b>by </b><i>, <a class="ref" href="polynom1.html#D14">POLYNOM1:def 14</a></i>;<br/>
<a NAME="E8:47_1_2"/>
<font color="Maroon">b1</font> <a href="polynom1.html#R3">divides</a> <font color="Maroon">b2</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E9:47_1_2"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</font>
 <b>by </b><i><a class="ref" href="groeb_1.html#T1" target="_self">Th1</a>, </i>;<br/>


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