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<a NAME="E1:143"/><span class="lab"><font color="Green" title="E104">A1</font></span>: 
130 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 5</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 13
 
;<br/>
<a NAME="E2:143"/><span class="lab"><font color="Green" title="E105">A2</font></span>: 
2,5,13 <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_distinct</a> 
 
;<br/>
<a NAME="E3:143"/>
( 130 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 13</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2 &amp; 130 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">13 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 5 )
 
;<br/>
<a NAME="E4:143"/><span class="kw">then </span>
( 2 <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> 130 &amp; 5 <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> 130 &amp; 13 <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> 130 )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:143"><span class="lab"><font color="Green" title="E104">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:143"/>
131 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 is  <a href="number08.html#V2" title="NUMBER08:attr.2">having_at_least_three_different_prime_divisors</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:143"><span class="lab"><font color="Green" title="E105">A2</font></span></a>, <a class="ref" href="xprimes1.html#T2" onmouseover="rs('xprimes1/T2')" onmouseout="rh()">XPRIMES1:2</a>, <a class="ref" href="xprimes1.html#T5" onmouseover="rs('xprimes1/T5')" onmouseout="rh()">XPRIMES1:5</a>, <a class="ref" href="xprimes1.html#T13" onmouseover="rs('xprimes1/T13')" onmouseout="rh()">XPRIMES1:13</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="number08.html#D9" target="_self" onmouseover="rs('number08/D9')" onmouseout="rh()">NUMBER08:def 9</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"> 131 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 is  <a href="number08.html#V2" title="NUMBER08:attr.2">having_at_least_three_different_prime_divisors</a> </span><br/>

<a NAME="E6:143"/><span class="lab"><font color="Green" title="E106">A3</font></span>: 
132 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 3</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 11
 
;<br/>
<a NAME="E7:143"/><span class="lab"><font color="Green" title="E107">A4</font></span>: 
2,3,11 <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_distinct</a> 
 
;<br/>
<a NAME="E8:143"/>
( 132 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 11</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2 &amp; 132 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">11 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 3 )
 
;<br/>
<a NAME="E9:143"/><span class="kw">then </span>
( 2 <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> 132 &amp; 3 <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> 132 &amp; 11 <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> 132 )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:143"><span class="lab"><font color="Green" title="E106">A3</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:143"/>
131 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 is  <a href="number08.html#V2" title="NUMBER08:attr.2">having_at_least_three_different_prime_divisors</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:143"><span class="lab"><font color="Green" title="E107">A4</font></span></a>, <a class="ref" href="xprimes1.html#T2" onmouseover="rs('xprimes1/T2')" onmouseout="rh()">XPRIMES1:2</a>, <a class="ref" href="xprimes1.html#T3" onmouseover="rs('xprimes1/T3')" onmouseout="rh()">XPRIMES1:3</a>, <a class="ref" href="xprimes1.html#T11" onmouseover="rs('xprimes1/T11')" onmouseout="rh()">XPRIMES1:11</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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