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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E1">Lm73</font></span>: <a NAME="T1"><span class="comment"><font color="firebrick">:: DUALSP03:1</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="normsp_1.html#V1" title="NORMSP_1:attr.1">strict</a>  <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b2">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X</font>  st (  for <font color="Olive" title="b3">f</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="dualsp01.html#K17" title="DUALSP01:func.17">DualSp</a> <font color="Olive" title="b1">X</font></span>)</span>  st (  for <font color="Olive" title="b4">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">A</font> holds <br/><span class="p1">(<span class="default"><a href="dualsp01.html#K14" title="DUALSP01:func.14">Bound2Lipschitz</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">X</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) holds <br/> <a href="dualsp01.html#K14" title="DUALSP01:func.14">Bound2Lipschitz</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">X</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="dualsp01.html#K17" title="DUALSP01:func.17">DualSp</a> <font color="Olive" title="b1">X</font></span>)</span> ) holds <br/> <a href="normsp_3.html#K19" title="NORMSP_3:func.19">ClNLin</a> <font color="Olive" title="b2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">X</font></div></div>
