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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E14">bagset2</font></span>: <a NAME="T14"><span class="comment"><font color="firebrick">:: FIELD_14:14</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">B</font> being   non  <a href="termord.html#V1" title="TERMORD:attr.1">zero</a>  <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">F</font><br/>  for <font color="Olive" title="b3">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> holds <br/> ( <font color="Olive" title="b2">B</font> <a href="pre_poly.html#R3" title="PRE_POLY:pred.3">divides</a>  <a href="ring_5.html#K1" title="RING_5:func.1">Bag</a> <font color="Olive" title="b3">S1</font> iff  ex <font color="Olive" title="b4">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="b2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ring_5.html#K1" title="RING_5:func.1">Bag</a> <font color="Olive" title="b4">S2</font> &amp; <font color="Olive" title="b4">S2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">S1</font> ) )</div></div>
