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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E49">lemgcd</font></span>: <a NAME="T45"><span class="comment"><font color="firebrick">:: FIELD_14:45</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">E</font> being   <a href="field_4.html#NM4" title="FIELD_4:NM.4">FieldExtension</a> of <font color="Olive" title="b1">F</font><br/>  for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</font> being    <a href="ring_4.html#M1" title="RING_4:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <font color="Olive" title="b1">F</font></span>)</span><br/>  for <font color="Olive" title="b5">p1</font>, <font color="Olive" title="b6">q1</font> being    <a href="ring_4.html#M1" title="RING_4:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <font color="Olive" title="b2">E</font></span>)</span>  st <font color="Olive" title="b5">p1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b3">p</font> &amp; <font color="Olive" title="b6">q1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b4">q</font> holds <br/><font color="Olive" title="b5">p1</font> <a href="ring_4.html#K12" title="RING_4:func.12">gcd</a> <font color="Olive" title="b6">q1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b3">p</font> <a href="ring_4.html#K12" title="RING_4:func.12">gcd</a> <font color="Olive" title="b4">q</font></div></div>
