<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E10">Th7</font></span>: <a NAME="T7"><span class="comment"><font color="firebrick">:: QUOFIELD:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font> being   non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>   <a href="vectsp_2.html#V1" title="VECTSP_2:attr.1">domRing-like</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">u</font>, <font color="Olive" title="b3">v</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="quofield.html#K1" title="QUOFIELD:func.1">Q.</a> <font color="Olive" title="b1">I</font>  st  ex <font color="Olive" title="b4">w</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="quofield.html#K7" title="QUOFIELD:func.7">Quot.</a> <font color="Olive" title="b1">I</font> st <br/>( <font color="Olive" title="b2">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">w</font> &amp; <font color="Olive" title="b3">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">w</font> ) holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b2">u</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">v</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">v</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">u</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a></span>)</span></div></div>
