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<a NAME="E1:21"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
<span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 10</span>)</span> <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 34 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p1">(<span class="default">10 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 34</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#T9" onmouseover="rs('newton/T9')" onmouseout="rh()">NEWTON:9</a></span>;<br/>
<a NAME="E2:21"/><span class="lab"><font color="Green" title="E22">A2</font></span>: 
1 <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#T24" onmouseover="rs('nat_d/T24')" onmouseout="rh()">NAT_D:24</a></span>;<br/>
2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 10 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><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> 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> 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> 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> 2</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2
<span class="kw">by</span> <span class="lab"><a class="ref" href="number02.html#T6" target="_self" onmouseover="rs('number02/T6')" onmouseout="rh()">Th6</a></span>
<br/>.= 
<span class="p1">(<span class="default">11 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 93</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1

;<br/>
<a NAME="E4:21"/><span class="kw">then </span>
<span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 10</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#D2" onmouseover="rs('nat_d/D2')" onmouseout="rh()">NAT_D:def 2</a></span>;<br/>
<a NAME="E5:21"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 10</span>)</span> <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 34</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton05.html#T15" onmouseover="rs('newton05/T15')" onmouseout="rh()">NEWTON05:15</a></span>;<br/>
<a NAME="E6:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A3</font></span>: 
2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 340,1 <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> 11
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="txt" href="#E2:21"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="ref" href="nat_d.html#T64" onmouseover="rs('nat_d/T64')" onmouseout="rh()">NAT_D:64</a></span>;<br/>
<span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p2">(<span class="default">340 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 340</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#T8" onmouseover="rs('newton/T8')" onmouseout="rh()">NEWTON:8</a></span>
<br/>.= 
2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 340</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>

;<br/>
<span class="kw">hence </span><a NAME="E8:21"/>
11 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 341</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:21"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="ref" href="int_2.html#T2" onmouseover="rs('int_2/T2')" onmouseout="rh()">INT_2:2</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/>


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