<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T4"><span class="comment"><font color="firebrick">:: DUALSP01:4</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of  <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> <br/>  for <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">w</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b4">v1</font>, <font color="Olive" title="b5">w1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="dualsp01.html#K4" title="DUALSP01:func.4">RVSp2RLSp</a> <font color="Olive" title="b1">X</font></span>)</span>  st <font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">v1</font> &amp; <font color="Olive" title="b3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">w1</font> holds <br/>( <font color="Olive" title="b2">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b5">w1</font> &amp; <font color="Olive" title="b2">v</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">v1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b5">w1</font> )</div></div>
