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<b>let </b><font color="Maroon">A</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="arytm_2.html#K1" target="_self">DEDEKIND_CUTS</a> , <font color="Maroon">B</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="arytm_2.html#K1" target="_self">DEDEKIND_CUTS</a> , <font color="Maroon">C</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="arytm_2.html#K1" target="_self">DEDEKIND_CUTS</a> ;<br/>

<a NAME="E1:37"/>
( <font color="Maroon">A</font> <a href="arytm_2.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="arytm_2.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="arytm_2.html#K5" target="_self">+</a> <font color="Maroon">B</font></span>)</span> <a href="arytm_2.html#K5" target="_self">+</a> <font color="Maroon">C</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="arytm_2.html#K5" target="_self">+</a> <font color="Maroon">B</font></span>)</span> <a href="arytm_2.html#K5" target="_self">+</a> <font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="arytm_2.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="arytm_2.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="arytm_2.html#E4"><i><font color="Green">Lemma34</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:37"/>
<font color="Maroon">A</font> <a href="arytm_2.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="arytm_2.html#K5" target="_self">+</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="arytm_2.html#K5" target="_self">+</a> <font color="Maroon">B</font></span>)</span> <a href="arytm_2.html#K5" target="_self">+</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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