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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" 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"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a></span>)</span> )</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" title="COMPLFLD:def.1">Def1</a></span>;<br/>
<a NAME="E2:21"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binop_2.html#K1" title="BINOP_2:func.1">-</a> <font color="Maroon" title="c2">z1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complfld.html#T2" target="_self" title="COMPLFLD:th.2">Th4</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:21"/><span class="lab"><font color="Green" title="E10">A2</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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a></span>)</span></span><br/>

<a NAME="E4:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A3</font></span>: 
<font color="Maroon" title="c2">z1</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">z</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complfld.html#T5" target="_self" title="COMPLFLD:th.5">Th7</a></span>;<br/>
<a NAME="E5:21"/>
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:21"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="vectsp_1.html#T28" title="VECTSP_1:th.28">VECTSP_1:28</a></span>;<br/>
<span class="kw">hence </span><span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  = 
<span class="p1">(<span class="default"><a href="binop_2.html#K1" title="BINOP_2:func.1">-</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:21"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="complfld.html#T5" target="_self" title="COMPLFLD:th.5">Th7</a></span>
<br/>.= 
 <a href="binop_2.html#K1" title="BINOP_2:func.1">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T222" title="XCMPLX_1:th.222">XCMPLX_1:222</a></span>
<br/>.= 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:21"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="complfld.html#T2" target="_self" title="COMPLFLD:th.2">Th4</a></span>
;<br/> <a class="txt" 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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