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<b>let </b><font color="Maroon" title="c2">B1</font>, <font color="Maroon" title="c3">B2</font> be   <a href="orders_1.html#NM2" title="ORDERS_1:NM.2">Order</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:129_1_2"/><i><font color="Green" title="E68">A13</font></i>: 
for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being  <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font> holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B1</font> iff <font color="Olive" title="b1">p</font> <a href="polynom1.html#R2" title="POLYNOM1:pred.2">&lt;='</a> <font color="Olive" title="b2">q</font> )
 <b>and </b><br/><a NAME="E2:129_1_2"/><i><font color="Green" title="E69">A14</font></i>: 
for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being  <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font> holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B2</font> iff <font color="Olive" title="b1">p</font> <a href="polynom1.html#R2" title="POLYNOM1:pred.2">&lt;='</a> <font color="Olive" title="b2">q</font> )
 ;<br/>

<b>let </b><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="relat_1.html#D2" title="RELAT_1:def.2">RELAT_1:def 2</a><br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:129_1_2_1"/><i><font color="Green" title="E70">A15</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B1</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c7">b2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:129_1_2_1"/><i><font color="Green" title="E71">A16</font></i>: 
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font> )
 <b>by </b><i><a class="ref" href="relset_1.html#T6" title="RELSET_1:th.6">RELSET_1:6</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c8">b1</font> = <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c9">b2</font> = <font color="Maroon" title="c7">b2</font> as   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font> <b>by </b><i><a class="txt" href="polynom1.html#E3:129_1_2_1"><i><font color="Green" title="E71">A16</font></i></a>, <a class="ref" href="polynom1.html#D14" target="_self" title="POLYNOM1:def.14">Def14</a></i>;<br/><a NAME="E5:129_1_2_1"/>
<font color="Maroon" title="c8">b1</font> <a href="polynom1.html#R2" title="POLYNOM1:pred.2">&lt;='</a> <font color="Maroon" title="c9">b2</font>
 <b>by </b><i><a class="txt" href="polynom1.html#E1:129_1_2"><i><font color="Green" title="E68">A13</font></i></a>, <a class="txt" href="polynom1.html#E1:129_1_2_1"><i><font color="Green" title="E70">A15</font></i></a>, <a class="txt" href="polynom1.html#E3:129_1_2_1"><i><font color="Green" title="E71">A16</font></i></a></i>;<br/><b>hence </b><a NAME="E6:129_1_2_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B2</font>
 <b>by </b><i><a class="txt" href="polynom1.html#E2:129_1_2"><i><font color="Green" title="E69">A14</font></i></a>, <a class="txt" href="polynom1.html#E3:129_1_2_1"><i><font color="Green" title="E71">A16</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E4:129_1_2"/><i><font color="Green" title="E70">A17</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B2</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c7">b2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:129_1_2"/><i><font color="Green" title="E71">A18</font></i>: 
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font> )
 <b>by </b><i><a class="ref" href="relset_1.html#T6" title="RELSET_1:th.6">RELSET_1:6</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">b1</font> = <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c9">b2</font> = <font color="Maroon" title="c7">b2</font> as   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font> <b>by </b><i><a class="txt" href="polynom1.html#E6:129_1_2"><i><font color="Green" title="E71">A18</font></i></a>, <a class="ref" href="polynom1.html#D14" target="_self" title="POLYNOM1:def.14">Def14</a></i>;<br/>
<a NAME="E8:129_1_2"/>
<font color="Maroon" title="c8">b1</font> <a href="polynom1.html#R2" title="POLYNOM1:pred.2">&lt;='</a> <font color="Maroon" title="c9">b2</font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E2:129_1_2"><i><font color="Green" title="E69">A14</font></i></a>, <a class="txt" href="polynom1.html#E4:129_1_2"><i><font color="Green" title="E70">A17</font></i></a>, <a class="txt" href="polynom1.html#E6:129_1_2"><i><font color="Green" title="E71">A18</font></i></a></i>;<br/>
<b>hence </b><a NAME="E9:129_1_2"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B1</font>
 <b>by </b><i><a class="txt" href="polynom1.html#E1:129_1_2"><i><font color="Green" title="E68">A13</font></i></a>, <a class="txt" href="polynom1.html#E6:129_1_2"><i><font color="Green" title="E71">A18</font></i></a></i>;<br/>


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