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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="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c2">a</font>, <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c3">b</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</a>  &amp; <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> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <span class="p1">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/>

<a NAME="E1:124"/>
<span class="p1">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton03.html#D5" onmouseover="rs('newton03/D5')" onmouseout="rh()">NEWTON03:def 5</a></span>;<br/>
<a NAME="E2:124"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <span class="p1">(<span class="default">2 <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <span class="p2">(<span class="default">2 <a href="newton03.html#K4" title="NEWTON03:func.4">|-count</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="wsierp_1.html#T12" onmouseover="rs('wsierp_1/T12')" onmouseout="rh()">WSIERP_1:12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:124"/>
(  <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c2">a</font>, <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c3">b</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</a>  &amp; <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> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <span class="p1">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c3">b</font></span>)</span> <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#D3" target="_self" onmouseover="rs('newton05/D3')" onmouseout="rh()">Def1</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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