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<b>let </b><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">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><a NAME="E1:67"/><i><font color="Green" title="E60">A1</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  &amp; <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  )
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c6">x0</font> = <font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c7">y0</font> = <font color="Maroon" title="c5">y</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  ;<br/>
<b>consider </b><font color="Maroon" title="c8">x'</font>, <font color="Maroon" title="c9">y'</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_3.html#K5" title="ARYTM_3:func.5">RAT+</a> <b> such that </b><br/><a NAME="E4:67"/><i><font color="Green" title="E61">A2</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">x'</font>
 <b>and </b><br/><a NAME="E5:67"/><i><font color="Green" title="E62">A3</font></i>: 
<font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">y'</font>
 <b>and </b><br/><a NAME="E6:67"/><i><font color="Green" title="E63">A4</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">x'</font> <a href="arytm_3.html#K9" title="ARYTM_3:func.9">+</a> <font color="Maroon" title="c9">y'</font>
 <b>by </b><i><a class="txt" href="arytm_2.html#E1:67"><i><font color="Green" title="E60">A1</font></i></a>, <a class="txt" href="arytm_2.html#E10"><i><font color="Green" title="E6">Lm5</font></i></a>, <a class="txt" href="arytm_2.html#E76"><i><font color="Green" title="E59">Lm47</font></i></a></i>;<br/>
<a NAME="E7:67"/>
<font color="Maroon" title="c8">x'</font> <a href="arytm_3.html#K9" title="ARYTM_3:func.9">+</a> <font color="Maroon" title="c9">y'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x0</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c7">y0</font>
 
<b>by </b><i><a class="txt" href="arytm_2.html#E4:67"><i><font color="Green" title="E61">A2</font></i></a>, <a class="txt" href="arytm_2.html#E5:67"><i><font color="Green" title="E62">A3</font></i></a>, <a class="txt" href="arytm_2.html#E74"><i><font color="Green" title="E57">Lm45</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:67"/>
<font color="Maroon" title="c5">y</font> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> 
 <b>by </b><i><a class="txt" href="arytm_2.html#E6:67"><i><font color="Green" title="E63">A4</font></i></a>, <a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>


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