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<span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</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"> (  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c2">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c3">b</font></span>)</span>) <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">a</font> &amp;  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c2">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c3">b</font></span>)</span>) <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c3">b</font> )</span><br/>

<a NAME="E1:112"/>
(  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c2">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c3">b</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c2">a</font> or  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c2">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c3">b</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c3">b</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#D9" onmouseover="rs('xxreal_0/D9')" onmouseout="rh()">XXREAL_0:def 9</a></span>;<br/>
<a NAME="E2:112"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A1</font></span>: 
(  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c2">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c3">b</font></span>)</span>) <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a>  <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c2">a</font> &amp;  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c2">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c3">b</font></span>)</span>) <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a>  <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c3">b</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#D9" onmouseover="rs('xxreal_0/D9')" onmouseout="rh()">XXREAL_0:def 9</a>, <a class="ref" href="newton05.html#T30" target="_self" onmouseover="rs('newton05/T30')" onmouseout="rh()">PEPIN31</a></span>;<br/>
<a NAME="E3:112"/>
(  <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c2">a</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">a</font> &amp;  <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c3">b</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c3">b</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton05.html#T24" target="_self" onmouseover="rs('newton05/T24')" onmouseout="rh()">Th3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:112"/>
(  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c2">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c3">b</font></span>)</span>) <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">a</font> &amp;  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c2">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c3">b</font></span>)</span>) <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c3">b</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:112"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="ref" href="int_2.html#T9" onmouseover="rs('int_2/T9')" onmouseout="rh()">INT_2:9</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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