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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds <br/> ( <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="waybel_6.html#K3" title="WAYBEL_6:func.3">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> iff <font color="Olive" title="b1">x</font> is  <a href="waybel_6.html#V6" title="WAYBEL_6:attr.6">co-prime</a>  )</span><br/><span class="kw">let </span><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>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="waybel_6.html#K3" title="WAYBEL_6:func.3">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> iff <font color="Maroon" title="c2">x</font> is  <a href="waybel_6.html#V6" title="WAYBEL_6:attr.6">co-prime</a>  )</span><br/>



<div><span class="kw">hereby </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">x</font> is  <a href="waybel_6.html#V6" title="WAYBEL_6:attr.6">co-prime</a>  implies <font color="Maroon" title="c2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="waybel_6.html#K3" title="WAYBEL_6:func.3">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> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:22_1"/>
<font color="Maroon" title="c2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="waybel_6.html#K3" title="WAYBEL_6:func.3">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>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> is  <a href="waybel_6.html#V6" title="WAYBEL_6:attr.6">co-prime</a> </span><br/><a NAME="E2:22_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="waybel_6.html#K3" title="WAYBEL_6:func.3">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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lattice3.html#D6" onmouseover="rs('lattice3/D6')" onmouseout="rh()">LATTICE3:def 6</a></span>;<br/><a NAME="E3:22_1"/><span class="kw">then </span>
<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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_6.html#D7" onmouseover="rs('waybel_6/D7')" onmouseout="rh()">WAYBEL_6:def 7</a></span>;<br/><span class="kw">hence </span><a NAME="E4:22_1"/>
<font color="Maroon" title="c2">x</font> is  <a href="waybel_6.html#V6" title="WAYBEL_6:attr.6">co-prime</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_6.html#D8" onmouseover="rs('waybel_6/D8')" onmouseout="rh()">WAYBEL_6:def 8</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:22"/>
<font color="Maroon" title="c2">x</font> is  <a href="waybel_6.html#V6" title="WAYBEL_6:attr.6">co-prime</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="waybel_6.html#K3" title="WAYBEL_6:func.3">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></span><br/>

<a NAME="E3:22"/><span class="kw">then </span>
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_6.html#D8" onmouseover="rs('waybel_6/D8')" onmouseout="rh()">WAYBEL_6:def 8</a></span>;<br/>
<a NAME="E4:22"/><span class="kw">then </span>
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="waybel_6.html#K3" title="WAYBEL_6:func.3">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_6.html#D7" onmouseover="rs('waybel_6/D7')" onmouseout="rh()">WAYBEL_6:def 7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:22"/>
<font color="Maroon" title="c2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="waybel_6.html#K3" title="WAYBEL_6:func.3">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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lattice3.html#D6" onmouseover="rs('lattice3/D6')" onmouseout="rh()">LATTICE3:def 6</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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