<?xml version="1.0"?>
<div class="add">

<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> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">X</font> holds  <span class="p1"><a href="csspace.html#K11" title="CSSPACE:func.11">||.</a><span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b1">x</font></span>)</span></span><a href="csspace.html#K11" title="CSSPACE:func.11">.||</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="csspace.html#K11" title="CSSPACE:func.11">||.</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="csspace.html#K11" title="CSSPACE:func.11">.||</a></span></span><br/><span class="kw">let </span><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" 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"> <span class="p1"><a href="csspace.html#K11" title="CSSPACE:func.11">||.</a><span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">x</font></span>)</span></span><a href="csspace.html#K11" title="CSSPACE:func.11">.||</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="csspace.html#K11" title="CSSPACE:func.11">||.</a><span class="default"><font color="Maroon" title="c5">x</font></span><a href="csspace.html#K11" title="CSSPACE:func.11">.||</a></span></span><br/>



<span class="p1"><a href="csspace.html#K11" title="CSSPACE:func.11">||.</a><span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">x</font></span>)</span></span><a href="csspace.html#K11" title="CSSPACE:func.11">.||</a></span> = 
<span class="p1"><a href="csspace.html#K11" title="CSSPACE:func.11">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">x</font></span>)</span></span><a href="csspace.html#K11" title="CSSPACE:func.11">.||</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_1.html#T3" onmouseover="rs('clvect_1/T3')" onmouseout="rh()">CLVECT_1:3</a></span>
<br/>.= 
<span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a></span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1"><a href="csspace.html#K11" title="CSSPACE:func.11">||.</a><span class="default"><font color="Maroon" title="c5">x</font></span><a href="csspace.html#K11" title="CSSPACE:func.11">.||</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="csspace.html#T43" target="_self" onmouseover="rs('csspace/T43')" onmouseout="rh()">Th38</a></span>
<br/>.= 
<span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1"><a href="csspace.html#K11" title="CSSPACE:func.11">||.</a><span class="default"><font color="Maroon" title="c5">x</font></span><a href="csspace.html#K11" title="CSSPACE:func.11">.||</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T52" onmouseover="rs('complex1/T52')" onmouseout="rh()">COMPLEX1:52</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E2:72"/>
<span class="p1"><a href="csspace.html#K11" title="CSSPACE:func.11">||.</a><span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">x</font></span>)</span></span><a href="csspace.html#K11" title="CSSPACE:func.11">.||</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="csspace.html#K11" title="CSSPACE:func.11">||.</a><span class="default"><font color="Maroon" title="c5">x</font></span><a href="csspace.html#K11" title="CSSPACE:func.11">.||</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T48" onmouseover="rs('complex1/T48')" onmouseout="rh()">COMPLEX1:48</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/>


</div>
