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<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font> be   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of  <a href="newton.html#K13" title="NEWTON:func.13">SetPrimes</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> is <a href="int_7.html#V1" title="INT_7:attr.1">prime-factorization-like</a> &amp; <font color="Maroon" title="c2">q</font> is <a href="int_7.html#V1" title="INT_7:attr.1">prime-factorization-like</a> &amp;  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c1">p</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c2">q</font> implies  <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c1">p</font>, <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c2">q</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_relative_prime</a>  )</span><br/>

<b>assume </b><a NAME="E1:20"/><i><font color="Green" title="E19">A1</font></i>: 
( <font color="Maroon" title="c1">p</font> is <a href="int_7.html#V1" title="INT_7:attr.1">prime-factorization-like</a> &amp; <font color="Maroon" title="c2">q</font> is <a href="int_7.html#V1" title="INT_7:attr.1">prime-factorization-like</a> &amp;  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c1">p</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c2">q</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c1">p</font>, <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c2">q</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_relative_prime</a> </span><br/>

<b>assume </b><a NAME="E2:20"/>
not  <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c1">p</font>, <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c2">q</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_relative_prime</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>then consider </b><font color="Maroon" title="c3">x</font> being  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E4:20"/><i><font color="Green" title="E20">A2</font></i>: 
( <font color="Maroon" title="c3">x</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a>  <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c1">p</font> &amp; <font color="Maroon" title="c3">x</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a>  <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c2">q</font> )
 <b>by </b><i><a class="ref" href="pythtrip.html#D2" title="PYTHTRIP:def.2">PYTHTRIP:def 2</a></i>;<br/>
<a NAME="E5:20"/><i><font color="Green" title="E21">A3</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="txt" href="int_7.html#E1:20"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="int_7.html#E4:20"><i><font color="Green" title="E20">A2</font></i></a>, <a class="txt" href="int_7.html#E14"><i><font color="Green" title="E14">Lm7</font></i></a></i>;<br/>
<a NAME="E6:20"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c2">q</font>
 
<b>by </b><i><a class="txt" href="int_7.html#E1:20"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="int_7.html#E4:20"><i><font color="Green" title="E20">A2</font></i></a>, <a class="txt" href="int_7.html#E14"><i><font color="Green" title="E14">Lm7</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:20"/>
contradiction
 <b>by </b><i><a class="txt" href="int_7.html#E1:20"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="int_7.html#E5:20"><i><font color="Green" title="E21">A3</font></i></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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