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<div><span class="kw">theorem </span><a NAME="T51"><span class="comment"><font color="firebrick">:: RING_4:51</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Olive" title="b1">F</font></span>)</span> holds <br/> ( <font color="Olive" title="b2">p</font> <a href="ring_4.html#K10" title="RING_4:func.10">gcd</a> <font color="Olive" title="b3">q</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Olive" title="b2">p</font> &amp; <font color="Olive" title="b2">p</font> <a href="ring_4.html#K10" title="RING_4:func.10">gcd</a> <font color="Olive" title="b3">q</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Olive" title="b3">q</font> &amp; (  for <font color="Olive" title="b4">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Olive" title="b1">F</font></span>)</span>  st <font color="Olive" title="b4">r</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Olive" title="b2">p</font> &amp; <font color="Olive" title="b4">r</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Olive" title="b3">q</font> holds <br/><font color="Olive" title="b4">r</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Olive" title="b2">p</font> <a href="ring_4.html#K10" title="RING_4:func.10">gcd</a> <font color="Olive" title="b3">q</font> ) ) <span class="kw">by</span> <span class="lab"><a class="ref" href="ring_4.html#D10" target="_self" onmouseover="rs('ring_4/D10')" onmouseout="rh()">defGCD</a></span>;<br/></div></div>
