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<b>let </b><font color="Maroon" title="c1">F</font>, <font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">H</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"> <font color="Maroon" title="c1">F</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">**</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">**</a> <font color="Maroon" title="c3">H</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">j</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#D8" title="MEMBERED:def.8">MEMBERED:def 8</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="c4">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c3">H</font></span>)</span> or <font color="Maroon" title="c4">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">**</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">**</a> <font color="Maroon" title="c3">H</font></span>)</span> )</span><br/>







<b>assume </b><a NAME="E1:144"/>
<font color="Maroon" title="c4">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c3">H</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="c4">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">**</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">**</a> <font color="Maroon" title="c3">H</font></span>)</span></span><br/>

<b>then consider </b><font color="Maroon" title="c5">w</font>, <font color="Maroon" title="c6">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> <b> such that </b><br/><a NAME="E3:144"/><i><font color="Green" title="E73">A1</font></i>: 
<font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">w</font> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <font color="Maroon" title="c6">w1</font>
 <b>and </b><br/><a NAME="E4:144"/><i><font color="Green" title="E74">A2</font></i>: 
<font color="Maroon" title="c5">w</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font>
 <b>and </b><br/><a NAME="E5:144"/><i><font color="Green" title="E75">A3</font></i>: 
<font color="Maroon" title="c6">w1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c3">H</font>
 ;<br/>
<a NAME="E6:144"/>
( <font color="Maroon" title="c6">w1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c6">w1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">H</font> )
 
<b>by </b><i><a class="txt" href="#E5:144"><i><font color="Green" title="E75">A3</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E7:144"/><b>then </b>
( <font color="Maroon" title="c5">w</font> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <font color="Maroon" title="c6">w1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">**</a> <font color="Maroon" title="c2">G</font> &amp; <font color="Maroon" title="c5">w</font> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <font color="Maroon" title="c6">w1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">**</a> <font color="Maroon" title="c3">H</font> )
 
<b>by </b><i><a class="txt" href="#E4:144"><i><font color="Green" title="E74">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:144"/>
<font color="Maroon" title="c4">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">**</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">**</a> <font color="Maroon" title="c3">H</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:144"><i><font color="Green" title="E73">A1</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</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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