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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"> ( <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> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  iff  <a href="newton05.html#K2" title="NEWTON05:func.2">parity</a> <font color="Maroon" title="c2">a</font> <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="c3">b</font> )</span><br/>

<span class="kw">thus </span><a NAME="E1:87"/>
( <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> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  implies  <a href="newton05.html#K2" title="NEWTON05:func.2">parity</a> <font color="Maroon" title="c2">a</font> <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="c3">b</font> )
  <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> <font color="Maroon" title="c2">a</font> <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="c3">b</font> implies <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> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="87_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:87_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> 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> <font color="Maroon" title="c2">a</font> <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="c3">b</font></span><br/>

<span class="kw">then </span> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  = 
 <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="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">b</font></span>)</span>

<br/>.= 
<span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="newton05.html#K2" title="NEWTON05:func.2">parity</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="newton05.html#K2" title="NEWTON05:func.2">parity</a> <font color="Maroon" title="c3">b</font></span>)</span></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="newton05.html#T54" target="_self" onmouseover="rs('newton05/T54')" onmouseout="rh()">ABP</a></span>
;<br/>
<a NAME="E3:87_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="newton05.html#K2" title="NEWTON05:func.2">parity</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="newton05.html#K2" title="NEWTON05:func.2">parity</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E4:87_1"/>
 <a href="newton05.html#K2" title="NEWTON05:func.2">parity</a> <font color="Maroon" title="c2">a</font> <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="c3">b</font>
 ; <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>

<span class="kw">assume </span><a NAME="E2:87"/>
 <a href="newton05.html#K2" title="NEWTON05:func.2">parity</a> <font color="Maroon" title="c2">a</font> <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="c3">b</font>
 ; <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"> <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> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a> </span><br/>

<span class="kw">then </span> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  = 
<span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="newton05.html#K2" title="NEWTON05:func.2">parity</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="newton05.html#K2" title="NEWTON05:func.2">parity</a> <font color="Maroon" title="c3">b</font></span>)</span></span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span>

<br/>.= 
 <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="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="newton05.html#T54" target="_self" onmouseover="rs('newton05/T54')" onmouseout="rh()">ABP</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:87"/>
<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> 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"> verum</span><br/>


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