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<b>let </b><font color="Maroon" title="c3">x'</font>, <font color="Maroon" title="c4">y'</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_3.html#K7" title="ARYTM_3:func.7">RAT+</a> ;<br/><b>let </b><font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c6">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_2.html#K2" title="ARYTM_2:func.2">REAL+</a> ;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:20"/><i><font color="Green" title="E21">A1</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x'</font>
 <b>and </b><br/><a NAME="E2:20"/><i><font color="Green" title="E22">A2</font></i>: 
<font color="Maroon" title="c6">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y'</font>
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:20_1"/>
<font color="Maroon" title="c5">x</font> <a href="arytm_2.html#R1" title="ARYTM_2:pred.1">&lt;='</a> <font color="Maroon" title="c6">y</font>
 ;<br/><a NAME="E2:20_1"/><b>then </b>
 ex <font color="Olive" title="b1">x'</font>, <font color="Olive" title="b2">y'</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_3.html#K7" title="ARYTM_3:func.7">RAT+</a>  st <br/>( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x'</font> &amp; <font color="Maroon" title="c6">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y'</font> &amp; <font color="Olive" title="b1">x'</font> <a href="arytm_3.html#R3" title="ARYTM_3:pred.3">&lt;='</a> <font color="Olive" title="b2">y'</font> )
 <b>by </b><i><a class="txt" href="arytm_2.html#E1:20"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="arytm_2.html#E2:20"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="arytm_2.html#D5" target="_self" title="ARYTM_2:def.5">Def5</a></i>;<br/><b>hence </b><a NAME="E3:20_1"/>
<font color="Maroon" title="c3">x'</font> <a href="arytm_3.html#R3" title="ARYTM_3:pred.3">&lt;='</a> <font color="Maroon" title="c4">y'</font>
 <b>by </b><i><a class="txt" href="arytm_2.html#E1:20"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="arytm_2.html#E2:20"><i><font color="Green" title="E22">A2</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E4:20"/>
( <font color="Maroon" title="c3">x'</font> <a href="arytm_3.html#R3" title="ARYTM_3:pred.3">&lt;='</a> <font color="Maroon" title="c4">y'</font> implies <font color="Maroon" title="c5">x</font> <a href="arytm_2.html#R1" title="ARYTM_2:pred.1">&lt;='</a> <font color="Maroon" title="c6">y</font> )
 <b>by </b><i><a class="txt" href="arytm_2.html#E1:20"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="arytm_2.html#E2:20"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="arytm_2.html#D5" target="_self" title="ARYTM_2:def.5">Def5</a></i>;<br/>


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