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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="E1:5"/>
<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/>

<b>then consider </b><font color="Maroon" title="c4">z1</font> being    <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> <b> such that </b><br/><a NAME="E3:5"/><i><font color="Green" title="E5">A1</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c4">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font>
 <b>by </b><i><a class="ref" href="arytm_2.html#T10" title="ARYTM_2:th.10">ARYTM_2:10</a></i>;<br/>
<b>assume </b><a NAME="E4:5"/>
<font color="Maroon" title="c3">y</font> <a href="arytm_2.html#R1" title="ARYTM_2:pred.1">&lt;='</a> <font color="Maroon" title="c2">x</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c5">z2</font> being    <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> <b> such that </b><br/><a NAME="E6:5"/><i><font color="Green" title="E6">A2</font></i>: 
<font color="Maroon" title="c3">y</font> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c5">z2</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_2.html#T10" title="ARYTM_2:th.10">ARYTM_2:10</a></i>;<br/>
<a NAME="E7:5"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c5">z2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="arytm_1.html#E3:5"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="arytm_1.html#E6:5"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="arytm_2.html#T7" title="ARYTM_2:th.7">ARYTM_2:7</a></i>;<br/>
<a NAME="E8:5"/><b>then </b>
<font color="Maroon" title="c4">z1</font> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <font color="Maroon" title="c5">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K13" title="ARYTM_3:func.13">{}</a> 
 
<b>by </b><i><a class="ref" href="arytm_1.html#T1" target="_self" title="ARYTM_1:th.1">Th1</a></i>;<br/>
<a NAME="E9:5"/><b>then </b>
<font color="Maroon" title="c4">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K13" title="ARYTM_3:func.13">{}</a> 
 
<b>by </b><i><a class="ref" href="arytm_2.html#T6" title="ARYTM_2:th.6">ARYTM_2:6</a></i>;<br/>
<b>hence </b><a NAME="E10:5"/>
<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#E3:5"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="arytm_2.html#D8" title="ARYTM_2:def.8">ARYTM_2:def 8</a></i>;<br/>


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