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<b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_2.html#K2" title="ARYTM_2:func.2">REAL+</a> ;<br/>



<b>assume </b><a NAME="E1:13"/><i><font color="Green" title="E13">A1</font></i>: 
not <font color="Maroon" title="c2">x</font> <a href="arytm_2.html#R1" title="ARYTM_2:pred.1">&lt;='</a> <font color="Maroon" title="c3">y</font>
 ;<br/>

<a NAME="E2:13"/><b>then </b><i><font color="Green" title="E14">A2</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="arytm_1.html#K1" title="ARYTM_1:func.1">-'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font>
 
<b>by </b><i><a class="ref" href="arytm_1.html#D1" target="_self" title="ARYTM_1:def.1">Def1</a></i>;<br/>
<b>assume </b><a NAME="E3:13"/>
<font color="Maroon" title="c2">x</font> <a href="arytm_1.html#K1" title="ARYTM_1:func.1">-'</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K13" title="ARYTM_3:func.13">{}</a> 
 ;<br/>

<a NAME="E4:13"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font>
 
<b>by </b><i><a class="txt" href="arytm_1.html#E2:13"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="arytm_2.html#D8" title="ARYTM_2:def.8">ARYTM_2:def 8</a></i>;<br/>
<b>hence </b><a NAME="E5:13"/>
contradiction
 <b>by </b><i><a class="txt" href="arytm_1.html#E1:13"><i><font color="Green" title="E13">A1</font></i></a></i>;<br/>


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