<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E22">Th24</font></span>: <a NAME="T24"><span class="comment"><font color="firebrick">:: VECTSP_2:24</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">x</font>, <font color="Olive" title="b3">y</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b4">v</font>, <font color="Olive" title="b5">w</font> being   <a href="vectsp_2.html#NM4" title="VECTSP_2:NM.4">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp_2.html#K3" title="VECTSP_2:func.3">RightModule</a> <font color="Olive" title="b1">R</font></span>)</span> holds <br/> ( <span class="p1">(<span class="default"><font color="Olive" title="b4">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b5">w</font></span>)</span> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">v</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <font color="Olive" title="b2">x</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">w</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <font color="Olive" title="b2">x</font></span>)</span> &amp; <font color="Olive" title="b4">v</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">v</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <font color="Olive" title="b2">x</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">v</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <font color="Olive" title="b3">y</font></span>)</span> &amp; <font color="Olive" title="b4">v</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b2">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">v</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <font color="Olive" title="b3">y</font></span>)</span> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <font color="Olive" title="b2">x</font> &amp; <font color="Olive" title="b4">v</font> <a href="vectsp_2.html#K4" title="VECTSP_2:func.4">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Olive" title="b1">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">v</font> )</div></div>
