<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">F</font>, <font color="Maroon" title="c2">G</font> be  <a href="membered.html#V2" title="MEMBERED:attr.2">ext-real-membered</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c2">G</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">i</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">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">G</font></span>)</span> or <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c2">G</font></span>)</span> ) &amp; (  not <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c2">G</font></span>)</span> or <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">G</font></span>)</span> ) )</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">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c2">G</font></span>)</span> or <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">G</font></span>)</span> )</span>
<div class="add"><b>assume </b><a NAME="E1:20_1"/>
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">G</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c2">G</font></span>)</span></span><br/><a NAME="E2:20_1"/><b>then </b>
 <a href="xxreal_3.html#K3" title="XXREAL_3:func.3">-</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">G</font>
 <b>by </b><i><a class="ref" href="member_1.html#T8" target="_self" title="MEMBER_1:th.8">Th8</a></i>;<br/><a NAME="E3:20_1"/><b>then </b>
(  <a href="xxreal_3.html#K3" title="XXREAL_3:func.3">-</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font> or  <a href="xxreal_3.html#K3" title="XXREAL_3:func.3">-</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E4:20_1"/><b>then </b>
( <font color="Maroon" title="c3">i</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="c1">F</font> or <font color="Maroon" title="c3">i</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">G</font> )
 <b>by </b><i><a class="ref" href="member_1.html#T8" target="_self" title="MEMBER_1:th.8">Th8</a></i>;<br/><b>hence </b><a NAME="E5:20_1"/>
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c2">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</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="E2:20"/>
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <font color="Maroon" title="c2">G</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">G</font></span>)</span></span><br/>

<a NAME="E3:20"/><b>then </b>
( <font color="Maroon" title="c3">i</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="c1">F</font> or <font color="Maroon" title="c3">i</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">G</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E4:20"/><b>then </b>
(  <a href="xxreal_3.html#K3" title="XXREAL_3:func.3">-</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font> or  <a href="xxreal_3.html#K3" title="XXREAL_3:func.3">-</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G</font> )
 
<b>by </b><i><a class="ref" href="member_1.html#T8" target="_self" title="MEMBER_1:th.8">Th8</a></i>;<br/>
<a NAME="E5:20"/><b>then </b>
 <a href="xxreal_3.html#K3" title="XXREAL_3:func.3">-</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">G</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:20"/>
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K1" title="MEMBER_1:func.1">--</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">G</font></span>)</span>
 <b>by </b><i><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>
