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<span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <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"> <span class="p1">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</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>  <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <font color="Maroon" title="c3">b</font></span>)</span></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:126_1"/>
( ( <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) or <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1"><span class="kw">suppose </span></a><a NAME="E1:126_1_1"/><span class="lab"><font color="Green" title="E47">A1</font></span>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</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"> <span class="p1">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</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>  <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <font color="Maroon" title="c3">b</font></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">a</font> = <font color="Maroon" title="c2">a</font> as   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> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c5">b</font> = <font color="Maroon" title="c3">b</font> as   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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:126_1_1"><span class="lab"><font color="Green" title="E47">A1</font></span></a></span>;<br/><a NAME="E4:126_1_1"/><span class="lab"><font color="Green" title="E48">A2</font></span>: 
 <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <span class="p2">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_2.html#D1" onmouseover="rs('nat_2/D1')" onmouseout="rh()">NAT_2:def 1</a></span>;<br/> <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <font color="Maroon" title="c5">b</font></span>)</span> = 
 <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c4">a</font></span>)</span></span>)</span> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span></span>)</span>

<br/>.= 
 <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton05.html#T87" target="_self" onmouseover="rs('newton05/T87')" onmouseout="rh()">OPC</a>, <a class="ref" href="newton03.html#T35" onmouseover="rs('newton03/T35')" onmouseout="rh()">NEWTON03:35</a></span>
<br/>.= 
 <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p4">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <span class="p4">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton05.html#T87" target="_self" onmouseover="rs('newton05/T87')" onmouseout="rh()">OPC</a>, <a class="ref" href="newton03.html#T35" onmouseover="rs('newton03/T35')" onmouseout="rh()">NEWTON03:35</a></span>
<br/>.= 
 <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p4">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton05.html#T87" target="_self" onmouseover="rs('newton05/T87')" onmouseout="rh()">OPC</a></span>
<br/>.= 
 <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p3">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <span class="p4">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <span class="p4">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton05.html#T87" target="_self" onmouseover="rs('newton05/T87')" onmouseout="rh()">OPC</a>, <a class="ref" href="newton03.html#T35" onmouseover="rs('newton03/T35')" onmouseout="rh()">NEWTON03:35</a></span>
<br/>.= 
 <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p3">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <span class="p4">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton05.html#T87" target="_self" onmouseover="rs('newton05/T87')" onmouseout="rh()">OPC</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p3">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <span class="p3">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton05.html#T28" target="_self" onmouseover="rs('newton05/T28')" onmouseout="rh()">ILO</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p2">(<span class="default"><a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <span class="p3">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton05.html#T41" target="_self" onmouseover="rs('newton05/T41')" onmouseout="rh()">PGG</a></span>
<br/>.= 
1 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <span class="p3">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton05.html#T27" target="_self" onmouseover="rs('newton05/T27')" onmouseout="rh()">OPA</a></span>
;<br/><span class="kw">hence </span><a NAME="E6:126_1_1"/>
<span class="p1">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</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>  <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <font color="Maroon" title="c3">b</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:126_1_1"><span class="lab"><font color="Green" title="E48">A2</font></span></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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_2"><span class="kw">suppose </span></a><a NAME="E1:126_1_2"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</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"> <span class="p1">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</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>  <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <font color="Maroon" title="c3">b</font></span>)</span></span><br/><div class="add"><a NAME="E2:126_1_2"/><span class="kw">then </span>
(  <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><font color="Maroon" title="c3">b</font></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> &amp; <span class="p1">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</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> <span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c3">b</font></span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_2.html#T12" onmouseover="rs('int_2/T12')" onmouseout="rh()">INT_2:12</a>, <a class="ref" href="newton02.html#T3" onmouseover="rs('newton02/T3')" onmouseout="rh()">NEWTON02:3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:126_1_2"/>
<span class="p1">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</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>  <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <font color="Maroon" title="c3">b</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="newton05.html#T88" target="_self" onmouseover="rs('newton05/T88')" onmouseout="rh()">OMO</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_3"><span class="kw">suppose </span></a><a NAME="E1:126_1_3"/>
<font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</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"> <span class="p1">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</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>  <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <font color="Maroon" title="c3">b</font></span>)</span></span><br/><div class="add"><a NAME="E2:126_1_3"/><span class="kw">then </span>
(  <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><font color="Maroon" title="c2">a</font></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> &amp; <span class="p1">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</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> <span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <font color="Maroon" title="c2">a</font></span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_2.html#T12" onmouseover="rs('int_2/T12')" onmouseout="rh()">INT_2:12</a>, <a class="ref" href="newton02.html#T3" onmouseover="rs('newton02/T3')" onmouseout="rh()">NEWTON02:3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:126_1_3"/>
<span class="p1">(<span class="default"><a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</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>  <a href="newton05.html#K4" title="NEWTON05:func.4">Oddity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <font color="Maroon" title="c3">b</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="newton05.html#T88" target="_self" onmouseover="rs('newton05/T88')" onmouseout="rh()">OMO</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></div><span class="kw">end;</span></div>

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