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<span class="kw">let </span><font color="Maroon" title="c1">z2</font>, <font color="Maroon" title="c2">z3</font>, <font color="Maroon" title="c3">z1</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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">z2</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>  &amp; <font color="Maroon" title="c2">z3</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="c3">z1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">z3</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c1">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z1</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z2</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c2">z3</font></span>)</span> )</span><br/>





<span class="kw">reconsider </span><font color="Maroon" title="c4">z19</font> = <font color="Maroon" title="c3">z1</font>, <font color="Maroon" title="c5">z29</font> = <font color="Maroon" title="c1">z2</font>, <font color="Maroon" title="c6">z39</font> = <font color="Maroon" title="c2">z3</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/>
<span class="kw">assume </span><a NAME="E2:74"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
<font color="Maroon" title="c1">z2</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="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">z3</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>  or <span class="p1">(<span class="default"><font color="Maroon" title="c3">z1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">z3</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c1">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z1</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z2</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c2">z3</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E3:74"/><span class="lab"><font color="Green" title="E11">A2</font></span>: 
<font color="Maroon" title="c2">z3</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="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">z1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">z3</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c1">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z1</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z2</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c2">z3</font></span>)</span></span><br/>

<a NAME="E4:74"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A3</font></span>: 
<font color="Maroon" title="c1">z2</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c2">z3</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="#E2:74"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="complfld.html#T62" target="_self" title="COMPLFLD:th.62">Th62</a></span>;<br/>
<a NAME="E5:74"/><span class="lab"><font color="Green" title="E13">A4</font></span>: 
<font color="Maroon" title="c1">z2</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c2">z3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">z29</font> <a href="binop_2.html#K6" title="BINOP_2:func.6">/</a> <font color="Maroon" title="c6">z39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:74"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="ref" href="complfld.html#T8" target="_self" title="COMPLFLD:th.8">Th8</a></span>;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c3">z1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">z3</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c1">z2</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">z19</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <font color="Maroon" title="c6">z39</font></span>)</span> <a href="binop_2.html#K6" title="BINOP_2:func.6">/</a> <font color="Maroon" title="c5">z29</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:74"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="complfld.html#T8" target="_self" title="COMPLFLD:th.8">Th8</a></span>
<br/>.= 
<font color="Maroon" title="c4">z19</font> <a href="binop_2.html#K6" title="BINOP_2:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z29</font> <a href="binop_2.html#K6" title="BINOP_2:func.6">/</a> <font color="Maroon" title="c6">z39</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T78" title="XCMPLX_1:th.78">XCMPLX_1:78</a></span>
<br/>.= 
<font color="Maroon" title="c3">z1</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z2</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c2">z3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:74"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="txt" href="#E4:74"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="complfld.html#T8" target="_self" title="COMPLFLD:th.8">Th8</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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