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<b>let </b><font color="Maroon">z</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>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>assume </b><a NAME="E1:36"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">z</font> <a href="arytm_2.html#R1">&lt;='</a> <font color="Maroon">y</font>
 ;<br/>

<a NAME="E2:36"/>
<font color="Maroon">y</font> <a href="arytm_2.html#R1">&lt;='</a> <font color="Maroon">x</font> <a href="arytm_2.html#K7">+</a> <font color="Maroon">y</font>
 
<b>by </b><i><a class="ref" href="arytm_2.html#T20">ARYTM_2:20</a></i>;<br/>
<a NAME="E3:36"/><b>then </b>
<font color="Maroon">z</font> <a href="arytm_2.html#R1">&lt;='</a> <font color="Maroon">x</font> <a href="arytm_2.html#K7">+</a> <font color="Maroon">y</font>
 
<b>by </b><i><a class="txt" href="arytm_1.html#E11"><i><font color="Green">Lemma27</font></i></a>, </i>;<br/>
<a NAME="E4:36"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="arytm_2.html#K7">+</a> <font color="Maroon">y</font></span>)</span> <a href="arytm_1.html#K2" target="_self">-</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="arytm_2.html#K7">+</a> <font color="Maroon">y</font></span>)</span> <a href="arytm_1.html#K1" target="_self">-'</a> <font color="Maroon">z</font>
 
<b>by </b><i><a class="ref" href="arytm_1.html#T8" target="_self">Th8</a></i>;<br/>
<b>hence </b><a NAME="E5:36"/>
<font color="Maroon">x</font> <a href="arytm_2.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="arytm_1.html#K1" target="_self">-'</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="arytm_2.html#K7">+</a> <font color="Maroon">y</font></span>)</span> <a href="arytm_1.html#K2" target="_self">-</a> <font color="Maroon">z</font>
 <b>by </b><i><a class="txt" href="arytm_1.html#E11"><i><font color="Green">Lemma27</font></i></a>, <a class="ref" href="arytm_1.html#T4" target="_self">Th4</a></i>;<br/>


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