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<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <font color="Maroon" title="c2">y</font> implies <font color="Maroon" title="c2">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <font color="Maroon" title="c1">x</font> ) &amp; (  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">y</font> implies  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <font color="Maroon" title="c2">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">x</font> ) )</span><br/>



<a NAME="E1:103"/>
( <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <font color="Maroon" title="c2">y</font> implies  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <span class="p1">(<span class="default"><a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <font color="Maroon" title="c1">x</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_3.html#T40" target="_self" title="XXREAL_3:th.40">Th40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:103"/>
( <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <font color="Maroon" title="c2">y</font> implies <font color="Maroon" title="c2">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <font color="Maroon" title="c1">x</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">y</font> implies  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <font color="Maroon" title="c2">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">x</font> )</span><br/>

<a NAME="E3:103"/>
(  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">y</font> implies  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <font color="Maroon" title="c2">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <span class="p1">(<span class="default"><a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <font color="Maroon" title="c1">x</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_3.html#T40" target="_self" title="XXREAL_3:th.40">Th40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:103"/>
(  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">y</font> implies  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <font color="Maroon" title="c2">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">x</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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