<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E16">Def6</font></span>   defines <a href="alggeo_1.html#K6" title="ALGGEO_1:func.6">Zero_</a> <a onclick="hs(this)" href="javascript:()">ALGGEO_1:def 5 : <br/></a><span> for <font color="Olive" title="b1">R</font> being   <a href="vectsp_2.html#NM2" title="VECTSP_2:NM.2">domRing</a><br/>  for <font color="Olive" title="b2">n</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a><br/>  for <font color="Olive" title="b3">S</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Polynom-Ring</a> (<font color="Olive" title="b2">n</font>,<font color="Olive" title="b1">R</font>)</span>)</span> holds <br/> ( ( <font color="Olive" title="b3">S</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="alggeo_1.html#K6" title="ALGGEO_1:func.6">Zero_</a> <font color="Olive" title="b3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b4">x</font> where <font color="Olive" title="b4">x</font> is   <a href="struct_0.html#NM5" title="STRUCT_0:NM.5">Function</a> of <font color="Olive" title="b2">n</font>,<font color="Olive" title="b1">R</font> :  for <font color="Olive" title="b5">p</font> being   <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Olive" title="b2">n</font>,<font color="Olive" title="b1">R</font>  st <font color="Olive" title="b5">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">S</font> holds <br/> <a href="polynom2.html#K2" title="POLYNOM2:func.2">eval</a> (<font color="Olive" title="b5">p</font>,<font color="Olive" title="b4">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">R</font> </span> } </span>  ) &amp; (  not <font color="Olive" title="b3">S</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="alggeo_1.html#K6" title="ALGGEO_1:func.6">Zero_</a> <font color="Olive" title="b3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) );<br/></span></div>
