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<div><span class="kw">theorem </span><a NAME="T15"><span class="comment"><font color="firebrick">:: EUCLID_7:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">B0</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds <br/> ( <font color="Olive" title="b1">B0</font> is  <a href="euclid_7.html#V1" title="EUCLID_7:attr.1">R-orthogonal</a>  iff  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being   <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">B0</font> &amp; <font color="Olive" title="b3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">B0</font> &amp; <font color="Olive" title="b2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">y</font> holds <br/><font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font> <a href="rvsum_1.html#R1" title="RVSUM_1:pred.1">are_orthogonal</a>  )</div></div>
