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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:24_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_6.html#K4" title="WAYBEL_6:func.4">PRIME</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a> </span>)</span>
 ;<br/><a NAME="E2:24_1"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_6.html#K4" title="WAYBEL_6:func.4">PRIME</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a> </span>)</span>
 <b>by </b><i><a class="ref" href="lattice3.html#D6" title="LATTICE3:def.6">LATTICE3:def 6</a></i>;<br/><a NAME="E3:24_1"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  is <a href="waybel_6.html#V5" title="WAYBEL_6:attr.5">prime</a>
 <b>by </b><i><a class="ref" href="waybel_6.html#D7" title="WAYBEL_6:def.7">WAYBEL_6:def 7</a></i>;<br/><b>hence </b><a NAME="E4:24_1"/>
<font color="Maroon" title="c2">x</font> is <a href="waybel_6.html#V6" title="WAYBEL_6:attr.6">co-prime</a>
 <b>by </b><i><a class="ref" href="waybel_6.html#D8" title="WAYBEL_6:def.8">WAYBEL_6:def 8</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:24"/>
<font color="Maroon" title="c2">x</font> is <a href="waybel_6.html#V6" title="WAYBEL_6:attr.6">co-prime</a>
 ;<br/>

<a NAME="E3:24"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  is <a href="waybel_6.html#V5" title="WAYBEL_6:attr.5">prime</a>
 
<b>by </b><i><a class="ref" href="waybel_6.html#D8" title="WAYBEL_6:def.8">WAYBEL_6:def 8</a></i>;<br/>
<a NAME="E4:24"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_6.html#K4" title="WAYBEL_6:func.4">PRIME</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="waybel_6.html#D7" title="WAYBEL_6:def.7">WAYBEL_6:def 7</a></i>;<br/>
<b>hence </b><a NAME="E5:24"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_6.html#K4" title="WAYBEL_6:func.4">PRIME</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a> </span>)</span>
 <b>by </b><i><a class="ref" href="lattice3.html#D6" title="LATTICE3:def.6">LATTICE3:def 6</a></i>;<br/>


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