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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E13">LM4</font></span>: <a NAME="T13"><span class="comment"><font color="firebrick">:: DUALSP04:13</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a><br/>  for <font color="Olive" title="b2">f</font> being   <a href="struct_0.html#NM4" title="STRUCT_0:NM.4">Function</a> of <font color="Olive" title="b1">X</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b3">g</font> being   <a href="struct_0.html#NM4" title="STRUCT_0:NM.4">Function</a> of <span class="p1">(<span class="default"><a href="dualsp04.html#K2" title="DUALSP04:func.2">RUSp2RNSp</a> <font color="Olive" title="b1">X</font></span>)</span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st <font color="Olive" title="b2">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b3">g</font> holds <br/>( <font color="Olive" title="b2">f</font> <a href="dualsp04.html#R3" title="DUALSP04:pred.3">is_Lipschitzian_on</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">X</font> iff <font color="Olive" title="b3">g</font> <a href="nfcont_1.html#R6" title="NFCONT_1:pred.6">is_Lipschitzian_on</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="dualsp04.html#K2" title="DUALSP04:func.2">RUSp2RNSp</a> <font color="Olive" title="b1">X</font></span>)</span> )</div></div>
