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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E27">Th45</font></span>: <a NAME="T45"><span class="comment"><font color="firebrick">:: REAL_NS2:45</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">Ar</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Olive" title="b1">n</font></span>)</span><br/>  for <font color="Olive" title="b3">At</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="b1">n</font></span>)</span><br/>  for <font color="Olive" title="b4">v</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Olive" title="b1">n</font></span>)</span><br/>  for <font color="Olive" title="b5">w</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b1">n</font></span>)</span>  st <font color="Olive" title="b2">Ar</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">At</font> &amp; <font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">w</font> &amp; <font color="Olive" title="b4">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Olive" title="b2">Ar</font> &amp; <font color="Olive" title="b2">Ar</font> is  <a href="rlaffin1.html#V1" title="RLAFFIN1:attr.1">affinely-independent</a>  holds <br/><font color="Olive" title="b4">v</font> <a href="rlaffin1.html#K5" title="RLAFFIN1:func.5">|--</a> <font color="Olive" title="b2">Ar</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b5">w</font> <a href="rlaffin1.html#K5" title="RLAFFIN1:func.5">|--</a> <font color="Olive" title="b3">At</font></div></div>
