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<span class="kw">let </span><font color="Maroon" title="c3">a</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="c3">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">a</font> is  not   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c4">b</font> = <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><font color="Maroon" title="c3">a</font></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  ;<br/>
<span class="lab"><font color="Green" title="E48">A1</font></span>: <font color="Maroon" title="c3">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">a</font> = 
<font color="Maroon" title="c3">a</font> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a> 

<br/>.= 
<span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><font color="Maroon" title="c3">a</font></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T75" onmouseover="rs('complex1/T75')" onmouseout="rh()">COMPLEX1:75</a></span>
<br/>.= 
<font color="Maroon" title="c4">b</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">b</font>

;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="110_2"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:110_2"/>
( <font color="Maroon" title="c4">b</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 2 or 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="110_2_1"><span class="kw">suppose </span></a><a NAME="E1:110_2_1"/>
<font color="Maroon" title="c4">b</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</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"> <font color="Maroon" title="c3">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">a</font> is  not   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a></span><br/><div class="add"><a NAME="E2:110_2_1"/><span class="kw">then </span>
( <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T23" onmouseover="rs('nat_1/T23')" onmouseout="rh()">NAT_1:23</a></span>;<br/><span class="kw">hence </span><a NAME="E3:110_2_1"/>
<font color="Maroon" title="c3">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">a</font> is  not   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:110"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="ref" href="int_2.html#D4" onmouseover="rs('int_2/D4')" onmouseout="rh()">INT_2:def 4</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="110_2_2"><span class="kw">suppose </span></a><a NAME="E1:110_2_2"/>
2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">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="c3">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">a</font> is  not   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a></span><br/><div class="add"><a NAME="E2:110_2_2"/><span class="kw">then </span>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/><a NAME="E3:110_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A2</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">b</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T68" onmouseover="rs('xreal_1/T68')" onmouseout="rh()">XREAL_1:68</a></span>;<br/><a NAME="E4:110_2_2"/>
<font color="Maroon" title="c4">b</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c4">b</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D3" onmouseover="rs('int_1/D3')" onmouseout="rh()">INT_1:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E5:110_2_2"/>
<font color="Maroon" title="c3">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">a</font> is  not   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:110"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E3:110_2_2"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="ref" href="int_2.html#D4" onmouseover="rs('int_2/D4')" onmouseout="rh()">INT_2:def 4</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></div><span class="kw">end;</span></div>

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