<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">z</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="E1:10"/>
<font color="Maroon" title="c2">x</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <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> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c4">z</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c5">z0</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="E3:10"/><i><font color="Green" title="E10">A1</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</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="c5">z0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c4">z</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="E4:10"/><i><font color="Green" title="E11">A2</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c6">x1</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="E6:10"/><i><font color="Green" title="E12">A3</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c6">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K12" title="ARYTM_3:func.12">one</a> 
 <b>by </b><i><a class="ref" href="arytm_2.html#T15" title="ARYTM_2:th.15">ARYTM_2:15</a></i>;<br/>
<font color="Maroon" title="c2">x</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c4">z</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c5">z0</font></span>)</span>
<b>by </b><i><a class="txt" href="arytm_1.html#E3:10"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="arytm_2.html#T16" title="ARYTM_2:th.16">ARYTM_2:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">x1</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c5">z0</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="arytm_1.html#E6:10"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="arytm_2.html#T13" title="ARYTM_2:th.13">ARYTM_2:13</a></i>
<br/>.= 
<font color="Maroon" title="c2">x</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="arytm_2.html#K7" title="ARYTM_2:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">x1</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c5">z0</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="arytm_2.html#T14" title="ARYTM_2:th.14">ARYTM_2:14</a></i>
;<br/>
<b>hence </b><a NAME="E8:10"/>
<font color="Maroon" title="c3">y</font> <a href="arytm_2.html#R1" title="ARYTM_2:pred.1">&lt;='</a> <font color="Maroon" title="c4">z</font>
 <b>by </b><i><a class="txt" href="arytm_1.html#E4:10"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="arytm_1.html#E3"><i><font color="Green" title="E2">Lm1</font></i></a>, <a class="ref" href="arytm_2.html#T20" title="ARYTM_2:th.20">ARYTM_2:20</a></i>;<br/>


</div>
