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<span class="kw">let </span><font color="Maroon" title="c1">h</font>, <font color="Maroon" title="c2">s</font> be   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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"> ( (  for <font color="Olive" title="b1">q</font> being   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a>  st <font color="Olive" title="b1">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#K13" title="NAT_3:func.13">prime_factorization</a> <font color="Maroon" title="c2">s</font></span>)</span> holds <br/> not <font color="Olive" title="b1">q</font>,<font color="Maroon" title="c1">h</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</a>  ) implies  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#K13" title="NAT_3:func.13">prime_factorization</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#K13" title="NAT_3:func.13">prime_factorization</a> <font color="Maroon" title="c1">h</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:7"/><span class="lab"><font color="Green" title="E8">A1</font></span>: 
 for <font color="Olive" title="b1">q</font> being   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a>  st <font color="Olive" title="b1">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#K13" title="NAT_3:func.13">prime_factorization</a> <font color="Maroon" title="c2">s</font></span>)</span> holds <br/> not <font color="Olive" title="b1">q</font>,<font color="Maroon" title="c1">h</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</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">  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#K13" title="NAT_3:func.13">prime_factorization</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#K13" title="NAT_3:func.13">prime_factorization</a> <font color="Maroon" title="c1">h</font></span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">x</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="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</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="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#K13" title="NAT_3:func.13">prime_factorization</a> <font color="Maroon" title="c2">s</font></span>)</span> or <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#K13" title="NAT_3:func.13">prime_factorization</a> <font color="Maroon" title="c1">h</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E2:7"/><span class="lab"><font color="Green" title="E9">A2</font></span>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#K13" title="NAT_3:func.13">prime_factorization</a> <font color="Maroon" title="c2">s</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"> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#K13" title="NAT_3:func.13">prime_factorization</a> <font color="Maroon" title="c1">h</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">q</font> = <font color="Maroon" title="c3">x</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="newton.html#D6" onmouseover="rs('newton/D6')" onmouseout="rh()">NEWTON:def 6</a></span>;<br/>
<a NAME="E4:7"/>
<font color="Maroon" title="c4">q</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c1">h</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_17.html#T5" target="_self" onmouseover="rs('group_17/T5')" onmouseout="rh()">Th5</a>, <a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="txt" href="#E1:7"><span class="lab"><font color="Green" title="E8">A1</font></span></a></span>;<br/>
<a NAME="E5:7"/><span class="kw">then </span>
<font color="Maroon" title="c4">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">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">h</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D13" onmouseover="rs('ordinal1/D13')" onmouseout="rh()">ORDINAL1:def 13</a>, <a class="ref" href="nat_3.html#T37" onmouseover="rs('nat_3/T37')" onmouseout="rh()">NAT_3:37</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:7"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#K13" title="NAT_3:func.13">prime_factorization</a> <font color="Maroon" title="c1">h</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_3.html#D9" onmouseover="rs('nat_3/D9')" onmouseout="rh()">NAT_3:def 9</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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