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<div><span class="kw">theorem </span><a NAME="T125"><span class="comment"><font color="firebrick">:: RVSUM_1:125</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b3">x1</font>, <font color="Olive" title="b4">x2</font>, <font color="Olive" title="b5">x3</font> being   <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b4">x2</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b4">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b5">x3</font> holds <br/><span class="p1"><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">|(</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">x</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Olive" title="b3">x1</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">y</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Olive" title="b4">x2</font></span>)</span></span>)</span>,<font color="Olive" title="b5">x3</font></span><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2"><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">|(</a><span class="default"><font color="Olive" title="b3">x1</font>,<font color="Olive" title="b5">x3</font></span><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">)|</a></span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2"><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">|(</a><span class="default"><font color="Olive" title="b4">x2</font>,<font color="Olive" title="b5">x3</font></span><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">)|</a></span></span>)</span></div></div>
