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<span class="kw">let </span><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font>, <font color="Maroon" title="c3">r</font>, <font color="Maroon" title="c4">s</font> be   <a href="xxreal_0.html#NM1" title="XXREAL_0:NM.1">ExtReal</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">s</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">p</font> implies <span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c4">s</font></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span> )</span><br/>







<span class="kw">assume </span><a NAME="E1:272"/><span class="lab"><font color="Green" title="E98">A1</font></span>: 
<font color="Maroon" title="c4">s</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">p</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c4">s</font></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">t</font> be   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="membered.html#D21" onmouseover="rs('membered/D21')" onmouseout="rh()">MEMBERED:def 21</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#K4" title="XXREAL_1:func.4">].</a><span class="default"><font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c4">s</font></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span> or  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#K4" title="XXREAL_1:func.4">].</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span> )</span><br/>

<span class="kw">assume </span><a NAME="E2:272"/>
<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#K4" title="XXREAL_1:func.4">].</a><span class="default"><font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c4">s</font></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#K4" title="XXREAL_1:func.4">].</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span></span><br/>

<a NAME="E3:272"/><span class="kw">then </span>
<font color="Maroon" title="c5">t</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_1.html#T4" target="_self" onmouseover="rs('xxreal_1/T4')" onmouseout="rh()">Th4</a></span>;<br/>
<a NAME="E4:272"/><span class="kw">then </span>
<font color="Maroon" title="c5">t</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:272"><span class="lab"><font color="Green" title="E98">A1</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:272"/>
 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#K4" title="XXREAL_1:func.4">].</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_1.html#T4" target="_self" onmouseover="rs('xxreal_1/T4')" onmouseout="rh()">Th4</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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