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<span class="kw">assume </span><a NAME="E1:26_1_1"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="member_1.html#K5" title="MEMBER_1:func.5">--</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="member_1.html#K4" title="MEMBER_1:func.4">--</a> <font color="Maroon" title="c2">F</font></span><br/>

<span class="kw">let </span><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> ; <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="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K5" title="MEMBER_1:func.5">--</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#K4" title="MEMBER_1:func.4">--</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#K4" title="MEMBER_1:func.4">--</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#K5" title="MEMBER_1:func.5">--</a> <font color="Maroon" title="c1">A</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="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K4" title="MEMBER_1:func.4">--</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#K5" title="MEMBER_1:func.5">--</a> <font color="Maroon" title="c1">A</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:26_1_1_1"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K5" title="MEMBER_1:func.5">--</a> <font color="Maroon" title="c1">A</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="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K4" title="MEMBER_1:func.4">--</a> <font color="Maroon" title="c2">F</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><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="E3:26_1_1_1"/>
 <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26_1_1_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="member_1.html#T12" target="_self" title="MEMBER_1:th.12">Th12</a></span>;<br/><span class="kw">hence </span><a NAME="E4:26_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#K4" title="MEMBER_1:func.4">--</a> <font color="Maroon" title="c2">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26_1_1"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="member_1.html#T2" target="_self" title="MEMBER_1:th.2">Th2</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="E3:26_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#K4" title="MEMBER_1:func.4">--</a> <font color="Maroon" title="c2">F</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="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K5" title="MEMBER_1:func.5">--</a> <font color="Maroon" title="c1">A</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><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> <span class="kw"> such that </span><br/><a NAME="E5:26_1_1"/><span class="lab"><font color="Green" title="E14">A3</font></span>: 
<font color="Maroon" title="c3">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="c4">w</font>
 <span class="kw">and </span><br/><a NAME="E6:26_1_1"/><span class="lab"><font color="Green" title="E15">A4</font></span>: 
<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/>
<span class="kw">reconsider </span><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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26_1_1"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E6:26_1_1"><span class="lab"><font color="Green" title="E15">A4</font></span></a></span>;<br/>
<a NAME="E8:26_1_1"/>
 <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_0.html#D2" title="XCMPLX_0:def.2">XCMPLX_0:def 2</a></span>;<br/>
<a NAME="E9:26_1_1"/><span class="kw">then </span>
 <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:26_1_1"><span class="lab"><font color="Green" title="E14">A3</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="E10:26_1_1"/><span class="kw">then </span>
 <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K5" title="MEMBER_1:func.5">--</a> <font color="Maroon" title="c1">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26_1_1"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E5:26_1_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E6:26_1_1"><span class="lab"><font color="Green" title="E15">A4</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:26_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#K5" title="MEMBER_1:func.5">--</a> <font color="Maroon" title="c1">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:26_1_1"><span class="lab"><font color="Green" title="E14">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/>


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