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<span class="kw">let </span><font color="Maroon" title="c2">a</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">  for <font color="Olive" title="b1">n</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds   <a href="newton05.html#K2" title="NEWTON05:func.2">parity</a> <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="Olive" title="b1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="newton05.html#K2" title="NEWTON05:func.2">parity</a> <font color="Maroon" title="c2">a</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">n</font> be   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</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#K2" title="NEWTON05:func.2">parity</a> <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="c3">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="newton05.html#K2" title="NEWTON05:func.2">parity</a> <font color="Maroon" title="c2">a</font></span><br/>



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="92_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="E1:92_1"/>
( <font color="Maroon" title="c2">a</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  or <font color="Maroon" title="c2">a</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">odd</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="92_1_1"><span class="kw">suppose </span></a><a NAME="E1:92_1_1"/><span class="lab"><font color="Green" title="E35">A1</font></span>: 
<font color="Maroon" title="c2">a</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</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#K2" title="NEWTON05:func.2">parity</a> <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="c3">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="newton05.html#K2" title="NEWTON05:func.2">parity</a> <font color="Maroon" title="c2">a</font></span><br/><div class="add"><a NAME="E2:92_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="c3">n</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a> 
 ;<br/><span class="kw">hence </span><a NAME="E3:92_1_1"/>
 <a href="newton05.html#K2" title="NEWTON05:func.2">parity</a> <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="c3">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="newton05.html#K2" title="NEWTON05:func.2">parity</a> <font color="Maroon" title="c2">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:92_1_1"><span class="lab"><font color="Green" title="E35">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="92_1_2"><span class="kw">suppose </span></a><a NAME="E1:92_1_2"/><span class="lab"><font color="Green" title="E35">A1</font></span>: 
<font color="Maroon" title="c2">a</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">odd</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#K2" title="NEWTON05:func.2">parity</a> <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="c3">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="newton05.html#K2" title="NEWTON05:func.2">parity</a> <font color="Maroon" title="c2">a</font></span><br/><div class="add"><a NAME="E2:92_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="c3">n</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">odd</a> 
 ;<br/><span class="kw">hence </span><a NAME="E3:92_1_2"/>
 <a href="newton05.html#K2" title="NEWTON05:func.2">parity</a> <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="c3">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="newton05.html#K2" title="NEWTON05:func.2">parity</a> <font color="Maroon" title="c2">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:92_1_2"><span class="lab"><font color="Green" title="E35">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><span class="kw">end;</span></div>

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