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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="abian.html#V1" title="ABIAN:attr.1">odd</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">  for <font color="Olive" title="b1">m</font> being   <a href="abian.html#V1" title="ABIAN:attr.1">odd</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds   <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Olive" title="b1">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Olive" title="b1">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">b</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">m</font> be   <a href="abian.html#V1" title="ABIAN:attr.1">odd</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">b</font></span>)</span></span><br/>



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="96_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="E1:96_1"/>
( <font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <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>  or <font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <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>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="96_1_1"><span class="kw">suppose </span></a><a NAME="E1:96_1_1"/><span class="lab"><font color="Green" title="E37">A1</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <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">  <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">b</font></span>)</span></span><br/><div class="add"><a NAME="E2:96_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c3">b</font>
 ;<br/><a NAME="E3:96_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="power.html#T2" onmouseover="rs('power/T2')" onmouseout="rh()">POWER:2</a></span>;<br/><span class="kw">hence </span><a NAME="E4:96_1_1"/>
 <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">b</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:96_1_1"><span class="lab"><font color="Green" title="E37">A1</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="96_1_2"><span class="kw">suppose </span></a><a NAME="E1:96_1_2"/><span class="lab"><font color="Green" title="E37">A1</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <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">  <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">b</font></span>)</span></span><br/><div class="add"><a NAME="E2:96_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c3">b</font>
 ;<br/><a NAME="E3:96_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="newton03.html#T13" onmouseover="rs('newton03/T13')" onmouseout="rh()">NEWTON03:13</a></span>;<br/><a NAME="E4:96_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="power.html#T2" onmouseover="rs('power/T2')" onmouseout="rh()">POWER:2</a></span>;<br/><a NAME="E5:96_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 ;<br/><a NAME="E6:96_1_2"/><span class="kw">then </span>
(  <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <span class="p1">(<span class="default">2 <a href="newton03.html#K4" title="NEWTON03:func.4">|-count</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <span class="p1">(<span class="default">2 <a href="newton03.html#K4" title="NEWTON03:func.4">|-count</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">b</font></span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:96_1_2"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="ref" href="newton05.html#D3" target="_self" onmouseover="rs('newton05/D3')" onmouseout="rh()">Def1</a></span>;<br/><span class="kw">hence </span><a NAME="E7:96_1_2"/>
 <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c4">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="newton05.html#K3" title="NEWTON05:func.3">Parity</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">b</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="newton03.html#T81" onmouseover="rs('newton03/T81')" onmouseout="rh()">NEWTON03:81</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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