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<span class="kw">assume </span><a NAME="E1:151_1_1"/><span class="lab"><font color="Green" title="E71">A1</font></span>: 
( <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> &amp; <font color="Maroon" title="c2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font> )
 ; <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">A</font> <a href="member_1.html#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="member_1.html#K12" title="MEMBER_1:func.12">**</a> <font color="Maroon" title="c4">G</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">a</font> be   <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="membered.html#D14" title="MEMBERED:def.14">MEMBERED:def 14</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="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> <a href="member_1.html#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c2">B</font> or <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F</font> <a href="member_1.html#K12" title="MEMBER_1:func.12">**</a> <font color="Maroon" title="c4">G</font> ) &amp; (  not <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F</font> <a href="member_1.html#K12" title="MEMBER_1:func.12">**</a> <font color="Maroon" title="c4">G</font> or <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> <a href="member_1.html#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c2">B</font> ) )</span><br/>

<div><span class="kw">hereby </span> <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="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F</font> <a href="member_1.html#K12" title="MEMBER_1:func.12">**</a> <font color="Maroon" title="c4">G</font> or <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> <a href="member_1.html#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c2">B</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:151_1_1_1"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> <a href="member_1.html#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c2">B</font>
 ; <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="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F</font> <a href="member_1.html#K12" title="MEMBER_1:func.12">**</a> <font color="Maroon" title="c4">G</font></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">c</font>, <font color="Maroon" title="c7">c1</font> being    <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"> such that </span><br/><a NAME="E3:151_1_1_1"/><span class="lab"><font color="Green" title="E72">A2</font></span>: 
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">c</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <font color="Maroon" title="c7">c1</font>
 <span class="kw">and </span><br/><a NAME="E4:151_1_1_1"/><span class="lab"><font color="Green" title="E73">A3</font></span>: 
( <font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> &amp; <font color="Maroon" title="c7">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> )
 ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c8">d1</font> = <font color="Maroon" title="c6">c</font>, <font color="Maroon" title="c9">d2</font> = <font color="Maroon" title="c7">c1</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K7" title="NUMBERS:func.7">ExtREAL</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:151_1_1_1"><span class="lab"><font color="Green" title="E73">A3</font></span></a>, <a class="ref" href="xxreal_0.html#D1" title="XXREAL_0:def.1">XXREAL_0:def 1</a></span>;<br/><a NAME="E6:151_1_1_1"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d1</font> <a href="member_1.html#K3" title="MEMBER_1:func.3">*</a> <font color="Maroon" title="c9">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:151_1_1_1"><span class="lab"><font color="Green" title="E72">A2</font></span></a>, <a class="txt" href="#E4:151_1_1_1"><span class="lab"><font color="Green" title="E73">A3</font></span></a>, <a class="ref" href="xxreal_3.html#D5" title="XXREAL_3:def.5">XXREAL_3:def 5</a></span>;<br/><span class="kw">hence </span><a NAME="E7:151_1_1_1"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F</font> <a href="member_1.html#K12" title="MEMBER_1:func.12">**</a> <font color="Maroon" title="c4">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:151_1_1"><span class="lab"><font color="Green" title="E71">A1</font></span></a>, <a class="txt" href="#E4:151_1_1_1"><span class="lab"><font color="Green" title="E73">A3</font></span></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/></div>
<span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E3:151_1_1"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F</font> <a href="member_1.html#K12" title="MEMBER_1:func.12">**</a> <font color="Maroon" title="c4">G</font>
 ; <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="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> <a href="member_1.html#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c2">B</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">w</font>, <font color="Maroon" title="c7">w1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K7" title="NUMBERS:func.7">ExtREAL</a> <span class="kw"> such that </span><br/><a NAME="E5:151_1_1"/><span class="lab"><font color="Green" title="E72">A4</font></span>: 
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">w</font> <a href="member_1.html#K3" title="MEMBER_1:func.3">*</a> <font color="Maroon" title="c7">w1</font>
 <span class="kw">and </span><br/><a NAME="E6:151_1_1"/><span class="lab"><font color="Green" title="E73">A5</font></span>: 
( <font color="Maroon" title="c6">w</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F</font> &amp; <font color="Maroon" title="c7">w1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">G</font> )
 ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">d1</font> = <font color="Maroon" title="c6">w</font>, <font color="Maroon" title="c9">d2</font> = <font color="Maroon" title="c7">w1</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="txt" href="#E1:151_1_1"><span class="lab"><font color="Green" title="E71">A1</font></span></a>, <a class="txt" href="#E6:151_1_1"><span class="lab"><font color="Green" title="E73">A5</font></span></a>, <a class="ref" href="xcmplx_0.html#D2" title="XCMPLX_0:def.2">XCMPLX_0:def 2</a></span>;<br/>
<a NAME="E8:151_1_1"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d1</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <font color="Maroon" title="c9">d2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:151_1_1"><span class="lab"><font color="Green" title="E71">A1</font></span></a>, <a class="txt" href="#E5:151_1_1"><span class="lab"><font color="Green" title="E72">A4</font></span></a>, <a class="txt" href="#E6:151_1_1"><span class="lab"><font color="Green" title="E73">A5</font></span></a>, <a class="ref" href="xxreal_3.html#D5" title="XXREAL_3:def.5">XXREAL_3:def 5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:151_1_1"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> <a href="member_1.html#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c2">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:151_1_1"><span class="lab"><font color="Green" title="E71">A1</font></span></a>, <a class="txt" href="#E6:151_1_1"><span class="lab"><font color="Green" title="E73">A5</font></span></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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