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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="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>

 <a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> <span class="p1">(<span class="default"><a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span>)</span>,<span class="p1">(<span class="default"><a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> <span class="p2">(<span class="default"><a href="arytm_0.html#K3" title="ARYTM_0:func.3">opp</a> <font color="Maroon" title="c4">x</font></span>)</span>,<span class="p2">(<span class="default"><a href="arytm_0.html#K3" title="ARYTM_0:func.3">opp</a> <font color="Maroon" title="c5">y</font></span>)</span></span>)</span> = 
 <a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> <font color="Maroon" title="c4">x</font>,<span class="p1">(<span class="default"><a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> <font color="Maroon" title="c5">y</font>,<span class="p2">(<span class="default"><a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> <span class="p3">(<span class="default"><a href="arytm_0.html#K3" title="ARYTM_0:func.3">opp</a> <font color="Maroon" title="c4">x</font></span>)</span>,<span class="p3">(<span class="default"><a href="arytm_0.html#K3" title="ARYTM_0:func.3">opp</a> <font color="Maroon" title="c5">y</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="arytm_0.html#T25" target="_self" title="ARYTM_0:th.25">Th25</a></i>
<br/>.= 
 <a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> <font color="Maroon" title="c4">x</font>,<span class="p1">(<span class="default"><a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> <span class="p2">(<span class="default"><a href="arytm_0.html#K3" title="ARYTM_0:func.3">opp</a> <font color="Maroon" title="c4">x</font></span>)</span>,<span class="p2">(<span class="default"><a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> <font color="Maroon" title="c5">y</font>,<span class="p3">(<span class="default"><a href="arytm_0.html#K3" title="ARYTM_0:func.3">opp</a> <font color="Maroon" title="c5">y</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="arytm_0.html#T25" target="_self" title="ARYTM_0:th.25">Th25</a></i>
<br/>.= 
 <a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> <font color="Maroon" title="c4">x</font>,<span class="p1">(<span class="default"><a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> <span class="p2">(<span class="default"><a href="arytm_0.html#K3" title="ARYTM_0:func.3">opp</a> <font color="Maroon" title="c4">x</font></span>)</span>,<font color="Maroon" title="c2">o</font></span>)</span>
<b>by </b><i><a class="ref" href="arytm_0.html#D4" target="_self" title="ARYTM_0:def.4">Def4</a></i>
<br/>.= 
 <a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> <font color="Maroon" title="c4">x</font>,<span class="p1">(<span class="default"><a href="arytm_0.html#K3" title="ARYTM_0:func.3">opp</a> <font color="Maroon" title="c4">x</font></span>)</span>
<b>by </b><i><a class="ref" href="arytm_0.html#T13" target="_self" title="ARYTM_0:th.13">Th13</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="ref" href="arytm_0.html#D4" target="_self" title="ARYTM_0:def.4">Def4</a></i>
;<br/>
<b>hence </b><a NAME="E2:30"/>
 <a href="arytm_0.html#K3" title="ARYTM_0:func.3">opp</a> <span class="p1">(<span class="default"><a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> <span class="p1">(<span class="default"><a href="arytm_0.html#K3" title="ARYTM_0:func.3">opp</a> <font color="Maroon" title="c4">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="arytm_0.html#K3" title="ARYTM_0:func.3">opp</a> <font color="Maroon" title="c5">y</font></span>)</span>
 <b>by </b><i><a class="ref" href="arytm_0.html#D4" target="_self" title="ARYTM_0:def.4">Def4</a></i>;<br/>


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