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<a NAME="E1:141_1_1"/>
 ex <font color="Olive" title="b1">S</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span> st <br/>(  <a href="pre_poly.html#K20" title="PRE_POLY:func.20">divisors</a> <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p1">(<span class="default"><a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Olive" title="b1">S</font>) &amp; (  for <font color="Olive" title="b2">p</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font> holds <br/> ( <font color="Olive" title="b2">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">S</font> iff <font color="Olive" title="b2">p</font> <a href="pre_poly.html#R3" title="PRE_POLY:pred.3">divides</a> <font color="Maroon" title="c2">b</font> ) ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D16" target="_self" onmouseover="rs('pre_poly/D16')" onmouseout="rh()">Def15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:141_1_1"/>
(  not  <a href="pre_poly.html#K20" title="PRE_POLY:func.20">divisors</a> <font color="Maroon" title="c2">b</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp;  <a href="pre_poly.html#K20" title="PRE_POLY:func.20">divisors</a> <font color="Maroon" title="c2">b</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</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"> verum</span><br/>


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