<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E1">Def1</font></span>   defines <a href="modcat_1.html#M1" title="MODCAT_1:mode.1">LeftMod_DOMAIN</a> <a onclick="hs(this)" href="javascript:()">MODCAT_1:def 1 : <br/></a><span> for <font color="Olive" title="b1">R</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive">b<sub>2</sub></font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds <br/> ( <font color="Olive">b<sub>2</sub></font> is    <a href="modcat_1.html#M1" title="MODCAT_1:mode.1">LeftMod_DOMAIN</a> of <font color="Olive" title="b1">R</font> iff  for <font color="Olive" title="b3">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive">b<sub>2</sub></font> holds  <font color="Olive" title="b3">x</font> is   <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a>  <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">LeftMod</a> of <font color="Olive" title="b1">R</font> );<br/></span></div>
