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<div><span class="kw">theorem </span><a NAME="T38"><span class="comment"><font color="firebrick">:: RFUNCT_2:38</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="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">h1</font>, <font color="Olive" title="b4">h2</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> holds <br/> ( ( <font color="Olive" title="b3">h1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">X</font> is  <a href="valued_0.html#V5" title="VALUED_0:attr.5">increasing</a>  &amp; <font color="Olive" title="b4">h2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b2">Y</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">V8</a>() implies <span class="p1">(<span class="default"><font color="Olive" title="b3">h1</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Olive" title="b4">h2</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Olive" title="b2">Y</font></span>)</span> is  <a href="valued_0.html#V5" title="VALUED_0:attr.5">increasing</a>  ) &amp; ( <font color="Olive" title="b3">h1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">X</font> is  <a href="valued_0.html#V6" title="VALUED_0:attr.6">decreasing</a>  &amp; <font color="Olive" title="b4">h2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b2">Y</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">V8</a>() implies <span class="p1">(<span class="default"><font color="Olive" title="b3">h1</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Olive" title="b4">h2</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Olive" title="b2">Y</font></span>)</span> is  <a href="valued_0.html#V6" title="VALUED_0:attr.6">decreasing</a>  ) )</div></div>
