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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E65">Th48</font></span>: <a NAME="T48"><span class="comment"><font color="firebrick">:: GRAPHSP:48</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">m</font>, <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b4">f</font>, <font color="Olive" title="b5">g</font>, <font color="Olive" title="b6">h</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>   st <font color="Olive" title="b5">g</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="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="graphsp.html#K18" title="GRAPHSP:func.18">Relax</a> <font color="Olive" title="b3">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p4">(<span class="default"><a href="graphsp.html#K15" title="GRAPHSP:func.15">findmin</a> <font color="Olive" title="b3">n</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> 1</span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Olive" title="b4">f</font> &amp; <font color="Olive" title="b6">h</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="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="graphsp.html#K18" title="GRAPHSP:func.18">Relax</a> <font color="Olive" title="b3">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p4">(<span class="default"><a href="graphsp.html#K15" title="GRAPHSP:func.15">findmin</a> <font color="Olive" title="b3">n</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Olive" title="b4">f</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="graphsp.html#K8" title="GRAPHSP:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K18" title="GRAPHSP:func.18">Relax</a> <font color="Olive" title="b3">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p2">(<span class="default"><a href="graphsp.html#K15" title="GRAPHSP:func.15">findmin</a> <font color="Olive" title="b3">n</font></span>)</span></span>)</span>,<font color="Olive" title="b4">f</font>,<font color="Olive" title="b3">n</font>) &amp; <font color="Olive" title="b2">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="graphsp.html#K13" title="GRAPHSP:func.13">UsedVx</a> (<font color="Olive" title="b5">g</font>,<font color="Olive" title="b3">n</font>) holds <br/><font color="Olive" title="b2">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="graphsp.html#K13" title="GRAPHSP:func.13">UsedVx</a> (<font color="Olive" title="b6">h</font>,<font color="Olive" title="b3">n</font>)</div></div>
