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<b>let </b><font color="Maroon" title="c1">i</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">i</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> iff <font color="Maroon" title="c1">i</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a>  is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> )</span><br/>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">i</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a>  is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> implies <font color="Maroon" title="c1">i</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> )</span>
<div class="add"><b>assume </b><a NAME="E1:14_1"/>
<font color="Maroon" title="c1">i</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">i</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a>  is <a href="abian.html#V1" title="ABIAN:attr.1">even</a></span><br/><b>then reconsider </b><font color="Maroon" title="c2">i'</font> = <font color="Maroon" title="c1">i</font> as  <a href="abian.html#V1" title="ABIAN:attr.1">even</a> <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ;<br/><a NAME="E3:14_1"/>
<font color="Maroon" title="c2">i'</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a>  is <a href="abian.html#V1" title="ABIAN:attr.1">even</a>
 ;<br/><b>hence </b><a NAME="E4:14_1"/>
<font color="Maroon" title="c1">i</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a>  is <a href="abian.html#V1" title="ABIAN:attr.1">even</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:14"/><i><font color="Green" title="E6">A1</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a>  is <a href="abian.html#V1" title="ABIAN:attr.1">even</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">i</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a></span><br/>

<b>assume </b><a NAME="E3:14"/>
not <font color="Maroon" title="c1">i</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>then reconsider </b><font color="Maroon" title="c2">i'</font> = <font color="Maroon" title="c1">i</font> as  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a> <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ;<br/>
<a NAME="E5:14"/>
not <font color="Maroon" title="c2">i'</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a>  is <a href="abian.html#V1" title="ABIAN:attr.1">even</a>
 
;<br/>
<b>hence </b><a NAME="E6:14"/>
contradiction
 <b>by </b><i><a class="txt" href="pythtrip.html#E2:14"><i><font color="Green" title="E6">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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