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<span class="kw">let </span><font color="Maroon" title="c1">z</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</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="c1">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> implies <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c2">z1</font> = <font color="Maroon" title="c1">z</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="complfld.html#D1" target="_self" onmouseover="rs('complfld/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:50"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
<font color="Maroon" title="c1">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a> </span><br/>

<a NAME="E3:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A2</font></span>: 
<font color="Maroon" title="c1">z</font> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complfld.html#T48" target="_self" onmouseover="rs('complfld/T48')" onmouseout="rh()">Th48</a></span>;<br/>
<a NAME="E4:50"/>
<font color="Maroon" title="c1">z</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">z1</font> <a href="xcmplx_0.html#K5" title="XCMPLX_0:func.5">"</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="complfld.html#T5" target="_self" onmouseover="rs('complfld/T5')" onmouseout="rh()">Th5</a></span>;<br/>
<span class="kw">hence </span><span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="complex1.html#K8" title="COMPLEX1:func.8">*'</a></span>)</span> <a href="xcmplx_0.html#K5" title="XCMPLX_0:func.5">"</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T36" onmouseover="rs('complex1/T36')" onmouseout="rh()">COMPLEX1:36</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:50"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="ref" href="complfld.html#T5" target="_self" onmouseover="rs('complfld/T5')" onmouseout="rh()">Th5</a></span>
;<br/> <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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