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<span class="kw">set </span><font color="Maroon" title="c3">f</font> =  <a href="number08.html#K3" title="NUMBER08:func.3">Euler_factorization_2</a> <font color="Maroon" title="c2">n</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">p</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="valued_0.html#D12" onmouseover="rs('valued_0/D12')" onmouseout="rh()">VALUED_0:def 12</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="c4">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K9" title="XTUPLE_0:func.9">proj1</a> <span class="p1">(<span class="default"><a href="number08.html#K3" title="NUMBER08:func.3">Euler_factorization_2</a> <font color="Maroon" title="c2">n</font></span>)</span> or <span class="p1">(<span class="default"><a href="number08.html#K3" title="NUMBER08:func.3">Euler_factorization_2</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">p</font> is  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:49_1_1"/><span class="lab"><font color="Green" title="E43">A1</font></span>: 
<font color="Maroon" title="c4">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="number08.html#K3" title="NUMBER08:func.3">Euler_factorization_2</a> <font color="Maroon" title="c2">n</font></span>)</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"> <span class="p1">(<span class="default"><a href="number08.html#K3" title="NUMBER08:func.3">Euler_factorization_2</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">p</font> is  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a> </span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">p</font> = <font color="Maroon" title="c4">p</font> as   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="number08.html#T29" target="_self" onmouseover="rs('number08/T29')" onmouseout="rh()">Th29</a></span>;<br/>
<a NAME="E3:49_1_1"/>
<span class="p1">(<span class="default"><a href="number08.html#K3" title="NUMBER08:func.3">Euler_factorization_2</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49_1_1"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="ref" href="number08.html#D3" target="_self" onmouseover="rs('number08/D3')" onmouseout="rh()">Def3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:49_1_1"/>
<span class="p1">(<span class="default"><a href="number08.html#K3" title="NUMBER08:func.3">Euler_factorization_2</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">p</font> is  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</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"> verum</span><br/>


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