<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T6"><span class="comment"><font color="firebrick">:: REALALG3:6</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">S</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">R</font>  st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b2">S</font>,<span class="p2"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">R</font></span>)</span></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span>,<span class="p2">(<span class="default"><a href="realalg1.html#K1" title="REALALG1:func.1">-</a> <font color="Olive" title="b2">S</font></span>)</span></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> is    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">R</font> &amp; <font color="Olive" title="b2">S</font> is  <a href="ideal_1.html#V1" title="IDEAL_1:attr.1">add-closed</a>  &amp; <font color="Olive" title="b2">S</font> is  <a href="realalg1.html#V5" title="REALALG1:attr.5">mult-closed</a>  holds <br/><font color="Olive" title="b2">S</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">R</font></span>)</span></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span> is  <a href="realalg1.html#V12" title="REALALG1:attr.12">positive_cone</a> </div></div>
