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<b>let </b><font color="Maroon" title="c4">X</font> be   <a href="csspace.html#NM1" title="CSSPACE:NM.1">ComplexUnitarySpace</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>, <font color="Olive" title="b2">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">X</font>  st <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="csspace.html#R1" title="CSSPACE:pred.1">are_orthogonal</a>  holds <br/> <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="csspace.html#R1" title="CSSPACE:pred.1">are_orthogonal</a> </span><br/><b>let </b><font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c6">y</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>,<font color="Maroon" title="c6">y</font> <a href="csspace.html#R1" title="CSSPACE:pred.1">are_orthogonal</a>  implies  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> <a href="csspace.html#R1" title="CSSPACE:pred.1">are_orthogonal</a>  )</span><br/>





<b>assume </b><a NAME="E1:60"/>
<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> <a href="csspace.html#R1" title="CSSPACE:pred.1">are_orthogonal</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> <a href="csspace.html#R1" title="CSSPACE:pred.1">are_orthogonal</a> </span><br/>

<a NAME="E2:60"/><b>then </b>
 <a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="csspace.html#K12" title="CSSPACE:func.12">.|.</a> <font color="Maroon" title="c6">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="csspace.html#D14" target="_self" title="CSSPACE:def.14">Def14</a></i>;<br/>
<a NAME="E3:60"/><b>then </b>
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="csspace.html#K12" title="CSSPACE:func.12">.|.</a> <font color="Maroon" title="c6">y</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="csspace.html#T25" target="_self" title="CSSPACE:th.25">Th25</a></i>;<br/>
<b>hence </b><a NAME="E4:60"/>
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font> <a href="csspace.html#R1" title="CSSPACE:pred.1">are_orthogonal</a> 
 <b>by </b><i><a class="ref" href="csspace.html#D14" target="_self" title="CSSPACE:def.14">Def14</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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