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<b>let </b><font color="Maroon" title="c4">X</font> be   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">X</font> holds  <font color="Olive" title="b1">x</font>, <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">X</font> <a href="bhsp_1.html#R1" title="BHSP_1:pred.1">are_orthogonal</a> </span><br/><b>let </b><font color="Maroon" title="c5">x</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">x</font>, <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">X</font> <a href="bhsp_1.html#R1" title="BHSP_1:pred.1">are_orthogonal</a> </span><br/>



<a NAME="E1:30"/>
<font color="Maroon" title="c5">x</font> <a href="bhsp_1.html#K2" title="BHSP_1:func.2">.|.</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c4">X</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="bhsp_1.html#T19" target="_self" title="BHSP_1:th.19">Th19</a></i>;<br/>
<b>hence </b><a NAME="E2:30"/>
<font color="Maroon" title="c5">x</font>, <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">X</font> <a href="bhsp_1.html#R1" title="BHSP_1:pred.1">are_orthogonal</a> 
 <b>by </b><i><a class="ref" href="bhsp_1.html#D3" target="_self" title="BHSP_1:def.3">Def3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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