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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>given </b><font color="Maroon">c<sub>2</sub></font> being  non <a href="xboole_0.html#V1">zero</a> <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> <b> such that </b><a NAME="E1:27"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 <b>and </b><br/><a NAME="E2:27"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> 2 <a href="nat_1.html#R1">divides</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="newton.html#NM1">Prime</a><b> such that </b><br/><a NAME="E4:27"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="moebius1.html#E1:27"><i><font color="Green">E21</font></i></a>, <a class="txt" href="moebius1.html#E5"><i><font color="Green">Lemma3</font></i></a></i>;<br/>
<a NAME="E5:27"/>
<font color="Maroon">c<sub>2</sub></font> is   <a href="nat_1.html#NM1">Nat</a>
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E6:27"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K2">|^</a> 2 <a href="nat_1.html#R1">divides</a> <font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> 2
 
<b>by </b><i><a class="txt" href="moebius1.html#E4:27"><i><font color="Green">E23</font></i></a>, <a class="ref" href="wsierp_1.html#T19">WSIERP_1:19</a></i>;<br/>
<a NAME="E7:27"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K2">|^</a> 2 <a href="nat_1.html#R1">divides</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="moebius1.html#E2:27"><i><font color="Green">E22</font></i></a>, <a class="ref" href="nat_1.html#T51">NAT_1:51</a></i>;<br/>
<b>hence </b><a NAME="E8:27"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="moebius1.html#V1" target="_self">square-containing</a>
 <b>by </b><i><a class="ref" href="moebius1.html#D1" target="_self">Def1</a></i>;<br/>


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