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<div><span class="kw">theorem </span><a NAME="T57"><span class="comment"><font color="firebrick">:: EUCLID_2:57</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">a</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</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="b3">p</font>,<font color="Olive" title="b4">q</font> <a href="rvsum_1.html#R1" title="RVSUM_1:pred.1">are_orthogonal</a>  holds <br/><font color="Olive" title="b3">p</font>,<font color="Olive" title="b2">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b4">q</font> <a href="rvsum_1.html#R1" title="RVSUM_1:pred.1">are_orthogonal</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid_2.html#T56" target="_self" onmouseover="rs('euclid_2/T56')" onmouseout="rh()">Th54</a></span>;<br/></div></div>
