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<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="arytm_3.html#R1" title="ARYTM_3:pred.1">are_relative_prime</a>  implies  <a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:34"/>
<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="arytm_3.html#R1" title="ARYTM_3:pred.1">are_relative_prime</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font></span><br/>

<a NAME="E2:34"/><span class="kw">then </span>
<font color="Maroon" title="c1">a</font> <a href="arytm_3.html#K3" title="ARYTM_3:func.3">hcf</a> <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="arytm_3.html#T25" target="_self" title="ARYTM_3:th.25">Th25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:34"/>
 <a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal3.html#T84" title="ORDINAL3:th.84">ORDINAL3:84</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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