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<b>assume </b><a NAME="E1:34_1_1"/><i><font color="Green" title="E20">A1</font></i>: 
<font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="member_1.html#K2" title="MEMBER_1:func.2">--</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c2">F</font></span><br/>

<b>let </b><font color="Maroon" title="c3">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> ; <i><font color="Red">:: according to </font></i><a class="ref" href="membered.html#D14" title="MEMBERED:def.14">MEMBERED:def 14</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  not <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K2" title="MEMBER_1:func.2">--</a> <font color="Maroon" title="c1">A</font> or <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c2">F</font> ) &amp; (  not <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c2">F</font> or <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K2" title="MEMBER_1:func.2">--</a> <font color="Maroon" title="c1">A</font> ) )</span><br/>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c2">F</font> or <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K2" title="MEMBER_1:func.2">--</a> <font color="Maroon" title="c1">A</font> )</span>
<div class="add"><b>assume </b><a NAME="E1:34_1_1_1"/><i><font color="Green" title="E21">A2</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K2" title="MEMBER_1:func.2">--</a> <font color="Maroon" title="c1">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c2">F</font></span><br/><b>then reconsider </b><font color="Maroon" title="c4">b</font> = <font color="Maroon" title="c3">a</font> as  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  ;<br/><a NAME="E3:34_1_1_1"/>
 <a href="xxreal_3.html#K3" title="XXREAL_3:func.3">-</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="txt" href="#E1:34_1_1_1"><i><font color="Green" title="E21">A2</font></i></a>, <a class="ref" href="member_1.html#T18" target="_self" title="MEMBER_1:th.18">Th18</a></i>;<br/><b>hence </b><a NAME="E4:34_1_1_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c2">F</font>
 <b>by </b><i><a class="txt" href="#E1:34_1_1"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="member_1.html#T8" target="_self" title="MEMBER_1:th.8">Th8</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E3:34_1_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c2">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K2" title="MEMBER_1:func.2">--</a> <font color="Maroon" title="c1">A</font></span><br/>

<b>then consider </b><font color="Maroon" title="c4">w</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> <b> such that </b><br/><a NAME="E5:34_1_1"/><i><font color="Green" title="E21">A3</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <font color="Maroon" title="c4">w</font>
 <b>and </b><br/><a NAME="E6:34_1_1"/><i><font color="Green" title="E22">A4</font></i>: 
<font color="Maroon" title="c4">w</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font>
 ;<br/>
<b>reconsider </b><font color="Maroon" title="c5">b</font> = <font color="Maroon" title="c4">w</font> as  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  <b>by </b><i><a class="txt" href="#E1:34_1_1"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="#E6:34_1_1"><i><font color="Green" title="E22">A4</font></i></a></i>;<br/>
<a NAME="E8:34_1_1"/>
 <a href="xxreal_3.html#K3" title="XXREAL_3:func.3">-</a> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> 
 
<b>by </b><i><a class="ref" href="xcmplx_0.html#D2" title="XCMPLX_0:def.2">XCMPLX_0:def 2</a></i>;<br/>
<a NAME="E9:34_1_1"/><b>then </b>
 <a href="xxreal_3.html#K3" title="XXREAL_3:func.3">-</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> 
 
<b>by </b><i><a class="txt" href="#E5:34_1_1"><i><font color="Green" title="E21">A3</font></i></a>, <a class="ref" href="xcmplx_0.html#D2" title="XCMPLX_0:def.2">XCMPLX_0:def 2</a></i>;<br/>
<a NAME="E10:34_1_1"/><b>then </b>
 <a href="xxreal_3.html#K3" title="XXREAL_3:func.3">-</a> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K2" title="MEMBER_1:func.2">--</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="txt" href="#E1:34_1_1"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="#E5:34_1_1"><i><font color="Green" title="E21">A3</font></i></a>, <a class="txt" href="#E6:34_1_1"><i><font color="Green" title="E22">A4</font></i></a></i>;<br/>
<b>hence </b><a NAME="E11:34_1_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K2" title="MEMBER_1:func.2">--</a> <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="txt" href="#E5:34_1_1"><i><font color="Green" title="E21">A3</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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