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<div><span class="kw">theorem </span><a NAME="T15"><span class="comment"><font color="firebrick">:: EUCLIDLP:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">s</font>, <font color="Olive" title="b2">t</font>, <font color="Olive" title="b3">u</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b4">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b5">x</font>, <font color="Olive" title="b6">y</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Olive" title="b4">n</font> holds  <font color="Olive" title="b5">x</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b3">u</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b6">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b5">x</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b6">y</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Olive" title="b2">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b6">y</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Olive" title="b3">u</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Olive" title="b6">y</font></span>)</span></div></div>
