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<div><span class="kw">theorem </span><a NAME="T7"><span class="comment"><font color="firebrick">:: PRSUBSET:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x</font> being   <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b1">x</font> is  <a href="partfun3.html#V1" title="PARTFUN3:attr.1">positive</a>  holds <br/> for <font color="Olive" title="b2">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">s</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">i</font> &amp; <font color="Olive" title="b2">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">x</font> holds <br/><span class="p1">(<span class="default"><a href="prsubset.html#K2" title="PRSUBSET:func.2">Q_ex</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>,<font color="Olive" title="b3">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="prsubset.html#K2" title="PRSUBSET:func.2">Q_ex</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">i</font>,<font color="Olive" title="b3">s</font>)</span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Olive" title="b2">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span> <a href="prsubset.html#K4" title="PRSUBSET:func.4">_le_</a> <font color="Olive" title="b3">s</font></span>)</span> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prsubset.html#K2" title="PRSUBSET:func.2">Q_ex</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">i</font>,<span class="p3">(<span class="default"><font color="Olive" title="b3">s</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><font color="Olive" title="b2">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>)</span>)</span></span>)</span></div></div>
