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<a NAME="E1:60_1_1"/><i><font color="Green">E51</font></i>: 
 <a href="arytm_3.html#K6" target="_self">RED</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K5">omega</a> 
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:60_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:60_1_1_1"/><b>then </b>
(  <a href="arytm_3.html#K6" target="_self">RED</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>, <a href="arytm_3.html#K6" target="_self">RED</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="arytm_3.html#R1" target="_self">are_relative_prime</a>  &amp;  <a href="arytm_3.html#K6" target="_self">RED</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i><a class="ref" href="arytm_3.html#T27" target="_self">Th27</a>, <a class="ref" href="arytm_3.html#T30" target="_self">Th30</a></i>;<br/><b>hence </b><a NAME="E3:60_1_1_1"/>
(  <a href="arytm_3.html#K6" target="_self">RED</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 implies <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="arytm_3.html#K6" target="_self">RED</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="arytm_3.html#K6" target="_self">RED</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="arytm_3.html#K7" target="_self">RAT+</a>  )
 <b>by </b><i><a class="ref" href="arytm_3.html#T39" target="_self">Th39</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:60_1_1"/>
( ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies  <a href="xboole_0.html#K1">{}</a>  is    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_3.html#K7" target="_self">RAT+</a>  ) &amp; (  <a href="arytm_3.html#K6" target="_self">RED</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1 implies  <a href="arytm_3.html#K6" target="_self">RED</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> is    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_3.html#K7" target="_self">RAT+</a>  ) &amp; ( not <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; not  <a href="arytm_3.html#K6" target="_self">RED</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1 implies <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="arytm_3.html#K6" target="_self">RED</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="arytm_3.html#K6" target="_self">RED</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> is    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_3.html#K7" target="_self">RAT+</a>  ) )
 <b>by </b><i><a class="txt" href="arytm_3.html#E1:60_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="arytm_3.html#T34" target="_self">Th34</a>, <a class="ref" href="ordinal2.html#T19">ORDINAL2:19</a></i>;<br/>


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