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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E3">Def8</font></span>   defines <a href="bhsp_5.html#M1" title="BHSP_5:mode.1">OrthogonalFamily</a> <a onclick="hs(this)" href="javascript:()">BHSP_5:def 8 : <br/></a><span> for <font color="Olive" title="b1">X</font> being   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a><br/>  for <font color="Olive">b<sub>2</sub></font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X</font> holds <br/> ( <font color="Olive">b<sub>2</sub></font> is    <a href="bhsp_5.html#M1" title="BHSP_5:mode.1">OrthogonalFamily</a> of <font color="Olive" title="b1">X</font> iff  for <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">y</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="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive" title="b4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive" title="b3">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">y</font> holds <br/><font color="Olive" title="b3">x</font> <a href="bhsp_1.html#K2" title="BHSP_1:func.2">.|.</a> <font color="Olive" title="b4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  );<br/></span></div>
