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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">i</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  iff  ex <font color="Olive" title="b1">j</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b1">j</font> )</span><br/>

<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">j</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b1">j</font> implies <font color="Maroon" title="c1">i</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:3_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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">j</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b1">j</font></span><br/><a NAME="E2:3_1"/><span class="kw">then </span>
2 <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c1">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="abian.html#D1" target="_self" title="ABIAN:def.1">Def1</a></span>;<br/><span class="kw">hence </span><a NAME="E3:3_1"/>
 ex <font color="Olive" title="b1">j</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b1">j</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D3" title="INT_1:def.3">INT_1:def 3</a></span>; <a class="txt" 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="E2:3"/>
 ex <font color="Olive" title="b1">j</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b1">j</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">hence </span><a NAME="E3:3"/>
2 <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c1">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D3" title="INT_1:def.3">INT_1:def 3</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="abian.html#D1" target="_self" title="ABIAN:def.1">ABIAN:def 1</a> <a class="txt" 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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