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<div><span class="kw">theorem </span><a NAME="T78"><span class="comment"><font color="firebrick">:: MATHMORP:78</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">t</font>, <font color="Olive" title="b2">s</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b3">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b4">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b3">n</font></span>)</span>  st <font color="Olive" title="b4">B</font> is  <a href="convex1.html#V1" title="CONVEX1:attr.1">convex</a>  &amp;  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">t</font> &amp;  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">s</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b2">s</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b1">t</font></span>)</span> <a href="mathmorp.html#K6" title="MATHMORP:func.6">(.)</a> <font color="Olive" title="b4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">s</font> <a href="mathmorp.html#K6" title="MATHMORP:func.6">(.)</a> <font color="Olive" title="b4">B</font></span>)</span> <a href="mathmorp.html#NK4" title="MATHMORP:NK.4">(+)</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">t</font> <a href="mathmorp.html#K6" title="MATHMORP:func.6">(.)</a> <font color="Olive" title="b4">B</font></span>)</span></div></div>
