<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T42"><span class="comment"><font color="firebrick">:: RMOD_3:42</font></span><br/></a><div class="add"> 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" title="b2">V</font> being   <a href="vectsp_2.html#V2" title="VECTSP_2:attr.2">strict</a>  <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">RightMod</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">W1</font>, <font color="Olive" title="b4">W2</font> being    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Olive" title="b2">V</font> holds <br/> ( <font color="Olive" title="b3">W1</font> <a href="rmod_3.html#K1" title="RMOD_3:func.1">+</a> <font color="Olive" title="b4">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">V</font> iff  for <font color="Olive" title="b5">v</font> being   <a href="vectsp_2.html#NM4" title="VECTSP_2:NM.4">Vector</a> of <font color="Olive" title="b2">V</font>  ex <font color="Olive" title="b6">v1</font>, <font color="Olive" title="b7">v2</font> being   <a href="vectsp_2.html#NM4" title="VECTSP_2:NM.4">Vector</a> of <font color="Olive" title="b2">V</font> st <br/>( <font color="Olive" title="b6">v1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b3">W1</font> &amp; <font color="Olive" title="b7">v2</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b4">W2</font> &amp; <font color="Olive" title="b5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b7">v2</font> ) ) <span class="kw">by</span> <span class="lab"><a class="txt" href="rmod_3.html#E55"><span class="lab"><font color="Green" title="E31">Lm14</font></span></a></span>;<br/></div></div>
