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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"> <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#K3" title="XBOOLE_0:func.3">/\</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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><span class="p2">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">q</font>)</span>)</span></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="xxreal_0.html#NM1" title="XXREAL_0:NM.1">ExtReal</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="membered.html#D14" onmouseover="rs('membered/D14')" onmouseout="rh()">MEMBERED:def 14</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> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</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> or <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"><span class="p2">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">q</font>)</span>)</span></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</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#K4" title="XXREAL_1:func.4">].</a><span class="default"><span class="p2">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">q</font>)</span>)</span></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span> or <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 href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</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">thus </span><a NAME="E1:143"/>
( <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 href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</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> implies <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"><span class="p2">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">q</font>)</span>)</span></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"><span class="p2">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">q</font>)</span>)</span></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span> or <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 href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</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><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="143_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:143_1"/><span class="lab"><font color="Green" title="E65">A1</font></span>: 
<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 href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</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>
 ; <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="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"><span class="p2">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">q</font>)</span>)</span></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span></span><br/>

<a NAME="E2:143_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A2</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" onmouseover="rs('xboole_0/D4')" onmouseout="rh()">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E3:143_1"/><span class="lab"><font color="Green" title="E67">A3</font></span>: 
<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="txt" href="#E1:143_1"><span class="lab"><font color="Green" title="E65">A1</font></span></a>, <a class="ref" href="xboole_0.html#D4" onmouseover="rs('xboole_0/D4')" onmouseout="rh()">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E4:143_1"/><span class="lab"><font color="Green" title="E68">A4</font></span>: 
<font color="Maroon" title="c3">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:143_1"><span class="lab"><font color="Green" title="E66">A2</font></span></a>, <a class="ref" href="xxreal_1.html#T4" target="_self" onmouseover="rs('xxreal_1/T4')" onmouseout="rh()">Th4</a></span>;<br/>
<a NAME="E5:143_1"/><span class="lab"><font color="Green" title="E69">A5</font></span>: 
<font color="Maroon" title="c5">t</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:143_1"><span class="lab"><font color="Green" title="E66">A2</font></span></a>, <a class="ref" href="xxreal_1.html#T4" target="_self" onmouseover="rs('xxreal_1/T4')" onmouseout="rh()">Th4</a></span>;<br/>
<a NAME="E6:143_1"/><span class="lab"><font color="Green" title="E70">A6</font></span>: 
<font color="Maroon" title="c1">p</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:143_1"><span class="lab"><font color="Green" title="E67">A3</font></span></a>, <a class="ref" href="xxreal_1.html#T4" target="_self" onmouseover="rs('xxreal_1/T4')" onmouseout="rh()">Th4</a></span>;<br/>
<a NAME="E7:143_1"/><span class="lab"><font color="Green" title="E71">A7</font></span>: 
<font color="Maroon" title="c5">t</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:143_1"><span class="lab"><font color="Green" title="E67">A3</font></span></a>, <a class="ref" href="xxreal_1.html#T4" target="_self" onmouseover="rs('xxreal_1/T4')" onmouseout="rh()">Th4</a></span>;<br/>
<a NAME="E8:143_1"/><span class="lab"><font color="Green" title="E72">A8</font></span>: 
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c1">p</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:143_1"><span class="lab"><font color="Green" title="E68">A4</font></span></a>, <a class="txt" href="#E6:143_1"><span class="lab"><font color="Green" title="E70">A6</font></span></a>, <a class="ref" href="xxreal_0.html#T29" onmouseover="rs('xxreal_0/T29')" onmouseout="rh()">XXREAL_0:29</a></span>;<br/>
<a NAME="E9:143_1"/>
<font color="Maroon" title="c5">t</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">q</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:143_1"><span class="lab"><font color="Green" title="E69">A5</font></span></a>, <a class="txt" href="#E7:143_1"><span class="lab"><font color="Green" title="E71">A7</font></span></a>, <a class="ref" href="xxreal_0.html#T21" onmouseover="rs('xxreal_0/T21')" onmouseout="rh()">XXREAL_0:21</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:143_1"/>
<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"><span class="p2">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">q</font>)</span>)</span></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:143_1"><span class="lab"><font color="Green" title="E72">A8</font></span></a>, <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/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:143"/><span class="lab"><font color="Green" title="E65">A9</font></span>: 
<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"><span class="p2">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">q</font>)</span>)</span></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"> <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 href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</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="E3:143"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A10</font></span>: 
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c1">p</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">t</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="E4:143"/><span class="lab"><font color="Green" title="E67">A11</font></span>: 
<font color="Maroon" title="c5">t</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c2">q</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:143"><span class="lab"><font color="Green" title="E65">A9</font></span></a>, <a class="ref" href="xxreal_1.html#T4" target="_self" onmouseover="rs('xxreal_1/T4')" onmouseout="rh()">Th4</a></span>;<br/>
<a NAME="E5:143"/><span class="lab"><font color="Green" title="E68">A12</font></span>: 
<font color="Maroon" title="c3">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:143"><span class="lab"><font color="Green" title="E66">A10</font></span></a>, <a class="ref" href="xxreal_0.html#T31" onmouseover="rs('xxreal_0/T31')" onmouseout="rh()">XXREAL_0:31</a></span>;<br/>
<a NAME="E6:143"/><span class="lab"><font color="Green" title="E69">A13</font></span>: 
<font color="Maroon" title="c1">p</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:143"><span class="lab"><font color="Green" title="E66">A10</font></span></a>, <a class="ref" href="xxreal_0.html#T31" onmouseover="rs('xxreal_0/T31')" onmouseout="rh()">XXREAL_0:31</a></span>;<br/>
<a NAME="E7:143"/><span class="lab"><font color="Green" title="E70">A14</font></span>: 
<font color="Maroon" title="c5">t</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:143"><span class="lab"><font color="Green" title="E67">A11</font></span></a>, <a class="ref" href="xxreal_0.html#T23" onmouseover="rs('xxreal_0/T23')" onmouseout="rh()">XXREAL_0:23</a></span>;<br/>
<a NAME="E8:143"/><span class="lab"><font color="Green" title="E71">A15</font></span>: 
<font color="Maroon" title="c5">t</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:143"><span class="lab"><font color="Green" title="E67">A11</font></span></a>, <a class="ref" href="xxreal_0.html#T23" onmouseover="rs('xxreal_0/T23')" onmouseout="rh()">XXREAL_0:23</a></span>;<br/>
<a NAME="E9:143"/><span class="lab"><font color="Green" title="E72">A16</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:143"><span class="lab"><font color="Green" title="E68">A12</font></span></a>, <a class="txt" href="#E7:143"><span class="lab"><font color="Green" title="E70">A14</font></span></a>, <a class="ref" href="xxreal_1.html#T4" target="_self" onmouseover="rs('xxreal_1/T4')" onmouseout="rh()">Th4</a></span>;<br/>
<a NAME="E10:143"/>
<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="txt" href="#E6:143"><span class="lab"><font color="Green" title="E69">A13</font></span></a>, <a class="txt" href="#E8:143"><span class="lab"><font color="Green" title="E71">A15</font></span></a>, <a class="ref" href="xxreal_1.html#T4" target="_self" onmouseover="rs('xxreal_1/T4')" onmouseout="rh()">Th4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:143"/>
<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 href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</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="txt" href="#E9:143"><span class="lab"><font color="Green" title="E72">A16</font></span></a>, <a class="ref" href="xboole_0.html#D4" onmouseover="rs('xboole_0/D4')" onmouseout="rh()">XBOOLE_0:def 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"> verum</span><br/>


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