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<span class="kw">let </span><font color="Maroon" title="c1">x1</font>, <font color="Maroon" title="c2">y1</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">  for <font color="Olive" title="b1">x2</font>, <font color="Olive" title="b2">y2</font> being   <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Maroon" title="c1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x2</font> &amp; <font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y2</font> &amp; <font color="Maroon" title="c2">y1</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> holds <br/><font color="Maroon" title="c1">x1</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x2</font> <a href="binop_2.html#K6" title="BINOP_2:func.6">/</a> <font color="Olive" title="b2">y2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">x2</font>, <font color="Maroon" title="c4">y2</font> be   <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</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">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font> &amp; <font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y2</font> &amp; <font color="Maroon" title="c2">y1</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 <font color="Maroon" title="c1">x1</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font> <a href="binop_2.html#K6" title="BINOP_2:func.6">/</a> <font color="Maroon" title="c4">y2</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:10"/><span class="lab"><font color="Green" title="E8">A1</font></span>: 
<font color="Maroon" title="c1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font>
 <span class="kw">and </span><br/><a NAME="E2:10"/><span class="lab"><font color="Green" title="E9">A2</font></span>: 
<font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">y1</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 <font color="Maroon" title="c1">x1</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font> <a href="binop_2.html#K6" title="BINOP_2:func.6">/</a> <font color="Maroon" title="c4">y2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E3:10"/>
<font color="Maroon" title="c2">y1</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"> <font color="Maroon" title="c1">x1</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font> <a href="binop_2.html#K6" title="BINOP_2:func.6">/</a> <font color="Maroon" title="c4">y2</font></span><br/>

<a NAME="E4:10"/><span class="kw">then </span>
<font color="Maroon" title="c2">y1</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y2</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="complfld.html#T5" target="_self" title="COMPLFLD:th.5">Th7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:10"/>
<font color="Maroon" title="c1">x1</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font> <a href="binop_2.html#K6" title="BINOP_2:func.6">/</a> <font color="Maroon" title="c4">y2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="ref" href="xcmplx_0.html#D9" title="XCMPLX_0:def.9">XCMPLX_0:def 9</a></span>; <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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