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<div><span class="kw">theorem </span><a NAME="T4"><span class="comment"><font color="firebrick">:: LOPBAN15:4</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">w</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="dualsp02.html#K3" title="DUALSP02:func.3">RNS_Real</a><br/>  for <font color="Olive" title="b3">v1</font>, <font color="Olive" title="b4">w1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>   st <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v1</font> &amp; <font color="Olive" title="b2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">w1</font> holds <br/><font color="Olive" title="b1">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Olive" title="b4">w1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="binop_2.html#D9" onmouseover="rs('binop_2/D9')" onmouseout="rh()">BINOP_2:def 9</a></span>;<br/></div></div>
