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<a NAME="E1:29"/>
 not 3 <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> 5
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="29_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:29_1"/>
3 <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> 5
 ; <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"> contradiction</span><br/>

<a NAME="E2:29_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A1</font></span>: 
5 <a href="int_1.html#K5" title="INT_1:func.5">mod</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pepin.html#T6" onmouseover="rs('pepin/T6')" onmouseout="rh()">PEPIN:6</a></span>;<br/>
<a NAME="E3:29_1"/>
5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 
;<br/>
<span class="kw">hence </span><a NAME="E4:29_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:29_1"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="nat_d.html#D2" onmouseover="rs('nat_d/D2')" onmouseout="rh()">NAT_D:def 2</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">hence </span><a NAME="E2:29"/>
 not 5 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 3 is  <a href="int_1.html#V1" title="INT_1:attr.1">integer</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="wsierp_1.html#T17" onmouseover="rs('wsierp_1/T17')" onmouseout="rh()">WSIERP_1:17</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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