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<span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="abian.html#V1" title="ABIAN:attr.1">even</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"> (  not 4 <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">a</font> implies  not <font color="Maroon" title="c2">a</font> is  <a href="pythtrip.html#V1" title="PYTHTRIP:attr.1">square</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:121"/><span class="lab"><font color="Green" title="E45">A1</font></span>: 
 not 4 <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">a</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">  not <font color="Maroon" title="c2">a</font> is  <a href="pythtrip.html#V1" title="PYTHTRIP:attr.1">square</a> </span><br/>

<a NAME="E2:121"/>
 not 2 <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="121_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:121_1"/>
2 <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 ; <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"> contradiction</span><br/>

<a NAME="E2:121_1"/><span class="kw">then </span>
2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2 <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton02.html#T2" onmouseover="rs('newton02/T2')" onmouseout="rh()">NEWTON02:2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:121_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:121"><span class="lab"><font color="Green" title="E45">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>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">b</font> = <font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 as   <a href="abian.html#V1" title="ABIAN:attr.1">odd</a>  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="abian.html#D1" onmouseover="rs('abian/D1')" onmouseout="rh()">ABIAN:def 1</a></span>;<br/>
<a NAME="E4:121"/>
 not 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">b</font> is  <a href="pythtrip.html#V1" title="PYTHTRIP:attr.1">square</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E5:121"/>
 not <font color="Maroon" title="c2">a</font> is  <a href="pythtrip.html#V1" title="PYTHTRIP:attr.1">square</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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