<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E52">simpAgcd1</font></span>: <a NAME="T50"><span class="comment"><font color="firebrick">:: FIELD_14:50</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">S1</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="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">F</font><br/>  for <font color="Olive" title="b3">p</font> being   <a href="ring_5.html#NM3" title="RING_5:NM.3">Ppoly</a> of <font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">S1</font><br/>  for <font color="Olive" title="b4">q</font> being   non  <a href="ratfunc1.html#V1" title="RATFUNC1:attr.1">constant</a>   <a href="ring_4.html#NV4" title="RING_4:NV.4">monic</a>  <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b1">F</font> holds <br/> ( <font color="Olive" title="b4">q</font> <a href="ring_4.html#R1" title="RING_4:pred.1">divides</a> <font color="Olive" title="b3">p</font> iff  ex <font color="Olive" title="b5">S2</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="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">F</font> st <br/>( <font color="Olive" title="b4">q</font> is   <a href="ring_5.html#NM3" title="RING_5:NM.3">Ppoly</a> of <font color="Olive" title="b1">F</font>,<font color="Olive" title="b5">S2</font> &amp; <font color="Olive" title="b5">S2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">S1</font> ) )</div></div>
