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<b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_2.html#K2">REAL+</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_2.html#K2">REAL+</a> ;<br/>



<b>reconsider </b><font color="Maroon">o</font> =  <a href="arytm_3.html#K13">{}</a>  as    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_2.html#K2">REAL+</a>  <b>by </b><i><a class="ref" href="arytm_2.html#T21">ARYTM_2:21</a></i>;<br/>
<b>assume </b><a NAME="E2:1"/>
<font color="Maroon">x</font> <a href="arytm_2.html#K7">+</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 ;<br/>

<a NAME="E3:1"/><b>then </b>
<font color="Maroon">x</font> <a href="arytm_2.html#K7">+</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> <a href="arytm_2.html#K7">+</a> <font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="arytm_2.html#D8">ARYTM_2:def 8</a></i>;<br/>
<b>hence </b><a NAME="E4:1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="arytm_3.html#K13">{}</a> 
 <b>by </b><i><a class="ref" href="arytm_2.html#T12">ARYTM_2:12</a></i>;<br/>


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