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<div>:: <span class="kw">deftheorem </span>   defines <a href="ringcat1.html#R2" title="RINGCAT1:pred.2">GO</a> <a onclick="hs(this)" href="javascript:()">RINGCAT1:def 15 : <br/></a><span> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> (  <a href="ringcat1.html#R2" title="RINGCAT1:pred.2">GO</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> iff  ex <font color="Olive" title="b3">x1</font>, <font color="Olive" title="b4">x2</font>, <font color="Olive" title="b5">x3</font>, <font color="Olive" title="b6">x4</font>, <font color="Olive" title="b7">x5</font>, <font color="Olive" title="b8">x6</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><span class="p2"><a href="xtuple_0.html#K6" title="XTUPLE_0:func.6">[</a><span class="default"><font color="Olive" title="b3">x1</font>,<font color="Olive" title="b4">x2</font>,<font color="Olive" title="b5">x3</font>,<font color="Olive" title="b6">x4</font></span><a href="xtuple_0.html#K6" title="XTUPLE_0:func.6">]</a></span>,<font color="Olive" title="b7">x5</font>,<font color="Olive" title="b8">x6</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> &amp;  ex <font color="Olive" title="b9">G</font> being   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a> st <br/>( <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b9">G</font> &amp; <font color="Olive" title="b3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b9">G</font> &amp; <font color="Olive" title="b4">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Olive" title="b9">G</font> &amp; <font color="Olive" title="b5">x3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">comp</a> <font color="Olive" title="b9">G</font> &amp; <font color="Olive" title="b6">x4</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="b9">G</font> &amp; <font color="Olive" title="b7">x5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Olive" title="b9">G</font> &amp; <font color="Olive" title="b8">x6</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Olive" title="b9">G</font> ) ) );<br/></span></div>
