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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>, <font color="Olive" title="b3">z</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="csspace.html#K10" title="CSSPACE:func.10">.|.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="csspace.html#K10" title="CSSPACE:func.10">.|.</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="csspace.html#K10" title="CSSPACE:func.10">.|.</a> <font color="Olive" title="b3">z</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c6">y</font>, <font color="Maroon" title="c7">z</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> <a href="csspace.html#K10" title="CSSPACE:func.10">.|.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">y</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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="c7">z</font></span>)</span></span><br/>







<span class="kw">thus </span><font color="Maroon" title="c5">x</font> <a href="csspace.html#K10" title="CSSPACE:func.10">.|.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">y</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">z</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">y</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">z</font></span>)</span> <a href="csspace.html#K10" title="CSSPACE:func.10">.|.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">*'</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="csspace.html#D13" target="_self" onmouseover="rs('csspace/D13')" onmouseout="rh()">Def11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">y</font> <a href="csspace.html#K10" title="CSSPACE:func.10">.|.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">z</font> <a href="csspace.html#K10" title="CSSPACE:func.10">.|.</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">*'</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="csspace.html#D13" target="_self" onmouseover="rs('csspace/D13')" onmouseout="rh()">Def11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">y</font> <a href="csspace.html#K10" title="CSSPACE:func.10">.|.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">*'</a></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">z</font> <a href="csspace.html#K10" title="CSSPACE:func.10">.|.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">*'</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T32" onmouseover="rs('complex1/T32')" onmouseout="rh()">COMPLEX1:32</a></span>
<br/>.= 
<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="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">z</font> <a href="csspace.html#K10" title="CSSPACE:func.10">.|.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">*'</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="csspace.html#D13" target="_self" onmouseover="rs('csspace/D13')" onmouseout="rh()">Def11</a></span>
<br/>.= 
<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="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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="c7">z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="csspace.html#D13" target="_self" onmouseover="rs('csspace/D13')" onmouseout="rh()">Def11</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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