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<span class="kw">let </span><font color="Maroon" title="c4">X</font> be   <a href="csspace.html#NM1" title="CSSPACE:NM.1">ComplexUnitarySpace</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/><font color="Olive" title="b1">x</font>, <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b2">y</font> <a href="csspace.html#R1" title="CSSPACE:pred.1">are_orthogonal</a> </span><br/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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 <font color="Maroon" title="c5">x</font>, <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c6">y</font> <a href="csspace.html#R1" title="CSSPACE:pred.1">are_orthogonal</a>  )</span><br/>





<span class="kw">assume </span><a NAME="E1:62"/>
<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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">x</font>, <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c6">y</font> <a href="csspace.html#R1" title="CSSPACE:pred.1">are_orthogonal</a> </span><br/>

<a NAME="E2:62"/><span class="kw">then </span>
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="csspace.html#K10" title="CSSPACE:func.10">.|.</a> <font color="Maroon" title="c6">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>
 
;<br/>
<span class="kw">hence </span><a NAME="E3:62"/>
<font color="Maroon" title="c5">x</font>, <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c6">y</font> <a href="csspace.html#R1" title="CSSPACE:pred.1">are_orthogonal</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="csspace.html#T24" target="_self" onmouseover="rs('csspace/T24')" onmouseout="rh()">Th19</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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