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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be   <a href="supinf_1.html#NM3" title="SUPINF_1:NM.3">R_eal</a>;<br/>



<a NAME="E1:38"/>
( <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <font color="Maroon" title="c2">y</font> implies  <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</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="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <font color="Maroon" title="c1">x</font> )
 
<b>by </b><i><a class="ref" href="supinf_2.html#T16" title="SUPINF_2:th.16">SUPINF_2:16</a></i>;<br/>
<b>hence </b><a NAME="E2:38"/>
( <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</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="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <font color="Maroon" title="c1">x</font> )
 ;<br/>

<a NAME="E3:38"/>
(  <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</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="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <font color="Maroon" title="c2">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <font color="Maroon" title="c1">x</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="supinf_2.html#T16" title="SUPINF_2:th.16">SUPINF_2:16</a></i>;<br/>
<b>hence </b><a NAME="E4:38"/>
(  <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</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="supinf_2.html#K3" title="SUPINF_2:func.3">-</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> )
 ;<br/>


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