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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E21">Th19</font></span>: <a NAME="T32"><span class="comment"><font color="firebrick">:: ANPROJ10:32</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">T</font> being   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a><br/>  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">T</font><br/>  for <font color="Olive" title="b4">p</font>, <font color="Olive" title="b5">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 1</span>)</span>  st <font color="Olive" title="b1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 1 &amp; <font color="Olive" title="b4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x</font> &amp; <font color="Olive" title="b5">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">y</font> holds <br/><font color="Olive" title="b2">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">p</font> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <font color="Olive" title="b5">q</font></div></div>
