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<b>let </b><font color="Maroon" title="c1">r</font>, <font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">s</font>, <font color="Maroon" title="c4">q</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">p</font> &amp; <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">s</font> implies  not <span class="p1"><a href="xxreal_1.html#K2" title="XXREAL_1:func.2">[.</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c3">s</font></span><a href="xxreal_1.html#K2" title="XXREAL_1:func.2">.[</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">].</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">q</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</a></span> )</span><br/>







<b>assume </b><b>that </b><br/><a NAME="E1:107"/><i><font color="Green" title="E60">A1</font></i>: 
<font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">p</font>
 <b>and </b><br/><a NAME="E2:107"/><i><font color="Green" title="E61">A2</font></i>: 
<font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">s</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <span class="p1"><a href="xxreal_1.html#K2" title="XXREAL_1:func.2">[.</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c3">s</font></span><a href="xxreal_1.html#K2" title="XXREAL_1:func.2">.[</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">].</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">q</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</a></span></span><br/>

<b>take </b><font color="Maroon" title="c5">t</font> = <font color="Maroon" title="c1">r</font>; <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"> ( <font color="Maroon" title="c5">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="xxreal_1.html#K2" title="XXREAL_1:func.2">[.</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c3">s</font></span><a href="xxreal_1.html#K2" title="XXREAL_1:func.2">.[</a></span> &amp; not <font color="Maroon" title="c5">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">].</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">q</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</a></span> )</span><br/>

<b>thus </b><a NAME="E3:107"/>
<font color="Maroon" title="c5">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="xxreal_1.html#K2" title="XXREAL_1:func.2">[.</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c3">s</font></span><a href="xxreal_1.html#K2" title="XXREAL_1:func.2">.[</a></span>
 <b>by </b><i><a class="txt" href="#E2:107"><i><font color="Green" title="E61">A2</font></i></a>, <a class="ref" href="xxreal_1.html#T3" target="_self" title="XXREAL_1:th.3">Th3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c5">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">].</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">q</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</a></span></span><br/>

<b>thus </b><a NAME="E4:107"/>
not <font color="Maroon" title="c5">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">].</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">q</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</a></span>
 <b>by </b><i><a class="txt" href="#E1:107"><i><font color="Green" title="E60">A1</font></i></a>, <a class="ref" href="xxreal_1.html#T2" target="_self" title="XXREAL_1:th.2">Th2</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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