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<span class="kw">let </span><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">n</font> be   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c1">m</font> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <font color="Maroon" title="c2">n</font> is  <a href="moebius1.html#V1" title="MOEBIUS1:attr.1">square-containing</a>  implies  not <font color="Maroon" title="c1">m</font> is  <a href="moebius1.html#V1" title="MOEBIUS1:attr.1">square-containing</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:36"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
not <font color="Maroon" title="c1">m</font> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <font color="Maroon" title="c2">n</font> is  <a href="moebius1.html#V1" title="MOEBIUS1:attr.1">square-containing</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not <font color="Maroon" title="c1">m</font> is  <a href="moebius1.html#V1" title="MOEBIUS1:attr.1">square-containing</a> </span><br/>

<span class="kw">assume </span><a NAME="E2:36"/>
<font color="Maroon" title="c1">m</font> is  <a href="moebius1.html#V1" title="MOEBIUS1:attr.1">square-containing</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">p</font> being   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a><span class="kw"> such that </span><br/><a NAME="E4:36"/><span class="lab"><font color="Green" title="E28">A2</font></span>: 
<font color="Maroon" title="c3">p</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 2 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">m</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="moebius1.html#D1" target="_self" title="MOEBIUS1:def.1">Def1</a></span>;<br/>
<a NAME="E5:36"/>
<font color="Maroon" title="c3">p</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 2 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">m</font> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <font color="Maroon" title="c2">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="ref" href="nat_d.html#T9" title="NAT_D:th.9">NAT_D:9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:36"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="moebius1.html#D1" target="_self" title="MOEBIUS1:def.1">Def1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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