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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E38">Th15</font></span>: <a NAME="T15"><span class="comment"><font color="firebrick">:: NUMBER09:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">m</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</a>  holds <br/> <a href="wsierp_1.html#K2" title="WSIERP_1:func.2">Product</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2"> { <span class="default"> <font color="Olive" title="b4">q</font> where <font color="Olive" title="b4">q</font> is   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a> : ( <font color="Olive" title="b4">q</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Olive" title="b3">m</font> &amp; <font color="Olive" title="b4">q</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Olive" title="b2">b</font> ) </span> } </span> </span>)</span>, <a href="wsierp_1.html#K2" title="WSIERP_1:func.2">Product</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2"> { <span class="default"> <font color="Olive" title="b4">r</font> where <font color="Olive" title="b4">r</font> is   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a> : ( <font color="Olive" title="b4">r</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Olive" title="b3">m</font> &amp;  not <font color="Olive" title="b4">r</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Olive" title="b1">a</font> &amp;  not <font color="Olive" title="b4">r</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Olive" title="b2">b</font> ) </span> } </span> </span>)</span> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</a> </div></div>
