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<span class="kw">let </span><font color="Maroon" title="c1">t</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"> (  not <font color="Maroon" title="c1">t</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> 24 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 2 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 3 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 4 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 6 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 8 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 12 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 24 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 24 )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c2">n</font> = <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><font color="Maroon" title="c1">t</font></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span> as   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> ;<br/>
<span class="kw">assume </span><a NAME="E2:5"/>
<font color="Maroon" title="c1">t</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> 24
 ; <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="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 2 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 3 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 4 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 6 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 8 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 12 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 24 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 24 )</span><br/>

<a NAME="E3:5"/><span class="kw">then </span>
<font color="Maroon" title="c2">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default">24</span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_2.html#T16" onmouseover="rs('int_2/T16')" onmouseout="rh()">INT_2:16</a></span>;<br/>
<a NAME="E4:5"/><span class="kw">then </span>
<font color="Maroon" title="c2">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> 24
 
;<br/>
<a NAME="E5:5"/><span class="kw">then </span>
( <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 or <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 or <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 24 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="number01.html#T3" target="_self" onmouseover="rs('number01/T3')" onmouseout="rh()">lem24nat</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:5"/>
( <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 2 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 3 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 4 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 6 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 8 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 12 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 24 or <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 24 )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="number01.html#T2" target="_self" onmouseover="rs('number01/T2')" onmouseout="rh()">lemmod</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/>


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