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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E68">Th71</font></span>: <a NAME="T71"><span class="comment"><font color="firebrick">:: RLAFFIN1:71</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">V</font> being   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a><br/>  for <font color="Olive" title="b3">v</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Olive" title="b2">V</font><br/>  for <font color="Olive" title="b4">I</font> being   <a href="rlaffin1.html#V1" title="RLAFFIN1:attr.1">affinely-independent</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b2">V</font>  st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Olive" title="b4">I</font> holds <br/>( <font color="Olive" title="b1">x</font> <a href="rlaffin1.html#K5" title="RLAFFIN1:func.5">|--</a> <font color="Olive" title="b4">I</font> is  <a href="convex1.html#V2" title="CONVEX1:attr.2">convex</a>  &amp;  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="rlaffin1.html#K5" title="RLAFFIN1:func.5">|--</a> <font color="Olive" title="b4">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">v</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="rlaffin1.html#K5" title="RLAFFIN1:func.5">|--</a> <font color="Olive" title="b4">I</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">v</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 )</div></div>
