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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>

<b>set </b><font color="Maroon" title="c3">f</font> =  <a href="nat_3.html#NK13" title="NAT_3:NK.13">pfexp</a> <font color="Maroon" title="c1">a</font>;<br/>
<b>set </b><font color="Maroon" title="c4">h</font> =  <a href="nat_3.html#NK13" title="NAT_3:NK.13">pfexp</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">b</font></span>)</span>;<br/>
<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:85"/><i><font color="Green" title="E47">A1</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#NK13" title="NAT_3:NK.13">pfexp</a> <font color="Maroon" title="c1">a</font></span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c6">x</font> = <font color="Maroon" title="c5">x</font> as   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a> <b>by </b><i><a class="ref" href="nat_3.html#T34" target="_self" title="NAT_3:th.34">Th34</a></i>;<br/>
<a NAME="E3:85"/><i><font color="Green" title="E48">A2</font></i>: 
<span class="p1">(<span class="default"><a href="nat_3.html#NK13" title="NAT_3:NK.13">pfexp</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="nat_3.html#E1:85"><i><font color="Green" title="E47">A1</font></i></a>, <a class="ref" href="polynom1.html#D7" title="POLYNOM1:def.7">POLYNOM1:def 7</a></i>;<br/>
<a NAME="E4:85"/><i><font color="Green" title="E49">A3</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 
<b>by </b><i><a class="ref" href="int_2.html#D5" title="INT_2:def.5">INT_2:def 5</a></i>;<br/>
<a NAME="E5:85"/><b>then </b><i><font color="Green" title="E50">A4</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="wsierp_1.html#K2" title="WSIERP_1:func.2">|^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">x</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">a</font>
 
<b>by </b><i><a class="ref" href="nat_3.html#D7" target="_self" title="NAT_3:def.7">Def7</a></i>;<br/>
<a NAME="E6:85"/>
<span class="p1">(<span class="default"><a href="nat_3.html#NK13" title="NAT_3:NK.13">pfexp</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <font color="Maroon" title="c1">a</font>
 
<b>by </b><i><a class="ref" href="nat_3.html#D8" target="_self" title="NAT_3:def.8">Def8</a></i>;<br/>
<a NAME="E7:85"/><b>then </b>
<font color="Maroon" title="c6">x</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c6">x</font> <a href="wsierp_1.html#K2" title="WSIERP_1:func.2">|^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">x</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <font color="Maroon" title="c1">a</font></span>)</span>
 
<b>by </b><i><a class="txt" href="nat_3.html#E3:85"><i><font color="Green" title="E48">A2</font></i></a>, <a class="ref" href="nat_3.html#T3" target="_self" title="NAT_3:th.3">Th3</a></i>;<br/>
<a NAME="E8:85"/><b>then </b>
<font color="Maroon" title="c6">x</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">a</font>
 
<b>by </b><i><a class="txt" href="nat_3.html#E5:85"><i><font color="Green" title="E50">A4</font></i></a>, <a class="ref" href="nat_d.html#T4" title="NAT_D:th.4">NAT_D:4</a></i>;<br/>
<a NAME="E9:85"/><b>then </b>
<font color="Maroon" title="c6">x</font> <a href="wsierp_1.html#K2" title="WSIERP_1:func.2">|^</a> 1 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">a</font>
 
<b>by </b><i><a class="ref" href="newton.html#T10" title="NEWTON:th.10">NEWTON:10</a></i>;<br/>
<a NAME="E10:85"/><b>then </b><i><font color="Green" title="E51">A5</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="wsierp_1.html#K2" title="WSIERP_1:func.2">|^</a> <span class="p1">(<span class="default">0 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">b</font>
 
<b>by </b><i><a class="ref" href="nat_d.html#T9" title="NAT_D:th.9">NAT_D:9</a></i>;<br/>
<a NAME="E11:85"/>
<span class="p1">(<span class="default"><a href="nat_3.html#NK13" title="NAT_3:NK.13">pfexp</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_3.html#D8" target="_self" title="NAT_3:def.8">Def8</a></i>;<br/>
<a NAME="E12:85"/><b>then </b>
<span class="p1">(<span class="default"><a href="nat_3.html#NK13" title="NAT_3:NK.13">pfexp</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="nat_3.html#E4:85"><i><font color="Green" title="E49">A3</font></i></a>, <a class="txt" href="nat_3.html#E10:85"><i><font color="Green" title="E51">A5</font></i></a>, <a class="ref" href="nat_3.html#D7" target="_self" title="NAT_3:def.7">Def7</a></i>;<br/>
<b>hence </b><a NAME="E13:85"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#NK13" title="NAT_3:NK.13">pfexp</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#D7" title="POLYNOM1:def.7">POLYNOM1:def 7</a></i>;<br/>


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