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<b>let </b><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">j</font> be  <a href="int_1.html#V1" title="INT_1:attr.1">integer</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</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="c2">j</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> ) iff <font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">j</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> )</span><br/>

<a NAME="E1:115"/>
( <font color="Maroon" title="c1">i</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> or  not <font color="Maroon" title="c1">i</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> )
 
;<br/>
<b>then consider </b><font color="Maroon" title="c3">i0</font> being  <a href="abian.html#V1" title="ABIAN:attr.1">even</a> <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>, <font color="Maroon" title="c4">i1</font> being  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a> <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:115"/><i><font color="Green" title="E63">A</font></i>: 
( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i0</font> or <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i1</font> )
 ;<br/>
<a NAME="E4:115"/>
( <font color="Maroon" title="c2">j</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> or  not <font color="Maroon" title="c2">j</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> )
 
;<br/>
<b>then consider </b><font color="Maroon" title="c5">j0</font> being  <a href="abian.html#V1" title="ABIAN:attr.1">even</a> <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>, <font color="Maroon" title="c6">j1</font> being  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a> <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E6:115"/><i><font color="Green" title="E64">B</font></i>: 
( <font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">j0</font> or <font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> )
 ;<br/>
<a NAME="E7:115"/>
( <font color="Maroon" title="c3">i0</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c5">j0</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> &amp; not <font color="Maroon" title="c3">i0</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">j1</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> &amp; not <font color="Maroon" title="c4">i1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c5">j0</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> &amp; <font color="Maroon" title="c4">i1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c6">j1</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> )
 
;<br/>
<b>hence </b><a NAME="E8:115"/>
( ( <font color="Maroon" title="c1">i</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> iff <font color="Maroon" title="c2">j</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> ) iff <font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">j</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> )
 <b>by </b><i><a class="txt" href="aofa_i00.html#E3:115"><i><font color="Green" title="E63">A</font></i></a>, <a class="txt" href="aofa_i00.html#E6:115"><i><font color="Green" title="E64">B</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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